Near the start of the Bayeux tapestry, five wriggly lines in red and blue represent the tide that washed Harold of Wessex ashore in France to be detained, and compromised, by William the Bastard, Duke of Normandy. Two years and many metres further on comes the episode in late September 1066 when, after weeks of waiting for the wind to change, William's army enjoys an easy crossing to Pevensey bay, men and horses confident and relaxed as their ships ride two wavy lines of gentle swell.

The Bayeux stitchwork makes La Manche or, if you like, the English Channel a running seam in the course of the narrative. It's the connection between opposing coasts. Not so 800 years later when Gustave Courbet, installed in a house on the beach at Etretat, looks out from Normandy into an overwhelming endlessness. Between him and the horizon, he sees a thunderous barrier, one breaker in particular rising and curling beneath a great shaggy wig of foam.

To Courbet, a native of Ornans near the Swiss border - as landlocked as anywhere in France - his "paysages de mer" as he called them, were confrontational yet wide open, enticing and, on a good day, massively and gloriously empathetic. Guy de Maupassant dropped in on him on one such day in the autumn of 1869. "In a big empty room, a huge man, corpulent and grubby, was using a kitchen knife to smear gobs of white paint on a big bare canvas. Every so often, he'd go and put his face to the window and stare at the storm. The sea came so close that it seemed to assail the house, covering it in spray and noise. The salt water beat like hail against the window panes and streamed down the walls." Swigging cider between bouts, the painter upped the turbulence. "Well," Maupassant added, "this work became The Wave, and it created quite a stir in the world."

Certainly, The Wave made waves. Courbet repeated the image over and over again. Wave-like, it kept on coming, and he gave successive versions resounding titles such as L'Eternité and (for a rare low-tide variation, now in the V&A) L'Immensité. The most famous, La Mer Orageuse, is in the Louvre. Others have ended up in museums in Bremen, Lyon, Edinburgh, Tokyo, Frankfurt, Winterthur and Berlin.

Being a romantic, Courbet took the wave personally. "In her fury," he told Victor Hugo, "she reminds me of a caged monster who can devour me. One feels carried away." His spuming prowess with the palette knife affected the young Cézanne: "It seems to hit you full in the chest. You stagger back, the whole room reeks of spray."

Impressionists by the Sea at the Royal Academy is to include Courbet's L'Eternité, a painting categorised "pre-impressionist" in an exhibition founded on the notion that a viable number of impressionist loans relating to the Normandy coast, eked out with comparable and more readily available pictures of other sorts ("salon" especially), is bound to be popular, surely. The theme may be catchpenny, but, bottom line, it's a guaranteed attraction.

Here we have the often-told story of fresh-air painting, ie impressionism, triumphing over stuffy conventionality. And, to help justify the inclusion of a number of so-so salon fillers, there's a makeweight subtext: these paintings are evidence of the changing socio-economics of the Normandy littoral from the mid-19th century onwards, a period in which fisheries declined somewhat and holidaymaking, made practicable by the coming of the railways, flourished. Promenades were extended, hotels took up prominent positions and, like cormorants, painters staked out every tasty viewpoint having discovered that pictures of bright-remembered coastal features, such as the rock arches of Etretat, were well-received in Paris and beyond. Even, would you believe it, on the other side of the Atlantic.

This being a summer show for the Royal Academy's top floor Sackler Galleries, it's something of a package deal. Restrictions apply. Forget 11th-century embroiderers, obviously, and any pre-pre-impressionists who happened to operate in the relevant area, such as Turner, whose Calais Pier, 1803, is a pier too early and too far north; and Richard Parkes Bonington, whose "easy brush and coquettish touch" (Delacroix's description) would have fitted in nicely had he been born 20 years later like Eugène-Louis Boudin, Trouville's leading painter in the pre-Monet years. Boudin, good old waspish Boudin, who had no time for Courbet ("He seems decidedly crude to me; little attention to detail"), officiates here as the godfather of seaside impressionism - he was the first to encourage Monet to desist from just doing cheeky caricatures of Le Havre personages and paint what lay within easy reach: "the sea, the light, the blue sky."

Boudin himself painted, repeatedly, the "ghastly masquerade" (his words) of "gilded parasites": lady visitors trailing along the front, including, on occasion, the Empress Eugénie, invariably the leading crinoline. These breezy frieze paintings set the tone. Here was the first-stop destination for railway passengers from Paris from the 1850s onwards. Alighting in Trouville, or adjacent watering places, served by the route down the Seine from the Gare St-Lazare, they were almost bound to feel, initially at least, zestful in the bright sea air.

Monet, of course, had been brought up in these parts, so for him there was no surprise at the end of the line. Yet in Normandy, more than in his later, more colourful, painting of resorts on the Mediterranean, he experienced the same exhilaration that had welled up in Courbet when, the cider getting to him and boisterousness besides, he pressed his nose against the window and torrential sea-spray stung his vision.

The term impressionism tends to blind us with its familiarity; it lulls us, it promises so exceedingly well, in a Classic FM sort of way. Yet, in the late 1870s, what we know of as impressionism nearly became intransigentism. It was a close call. Had the label stuck, L'Exposition d'Impressionists, 1877, would have been L'Exposition d'Intransigeants, and we would now be warming to the prospect of getting round to seeing Intransigents By the Sea at the Royal Academy.

With one word, the whole complexion of the movement, or public perception of it, would have altered. Courbet the reckless, exhibitionistic, pioneer would have gained recognition as one of them; Monet would be admired not as a painter of so many agreeable pictures of delightful spots, but as the noble spirit of persistence, doggedly working from the life. Just one word and, on the Normandy coast, from Dieppe southwards, paintings of potted geraniums on terraces, of people mooching on shingle or braving the surf, would be seen not as pictorial evidence of an expanding leisure industry, but as bold departures.

Exhibition curators can learn a lot from the Bayeux tapestry. It runs rhythmically, scenically, busy yet uncluttered, with marginal strands to complement the action and attention directed, throughout, on marvellous incidents and crucial events. How does this translate to 19th-century Normandy and issues raised by Impressionists by the Sea? Well, for one thing it marginalises the Troyons and Hereaus: those whose rightful resting place is the French provincial museum. For another, it gives the chief protagonists room in which to conduct themselves, dashingly, subtly, at times heroically. Forecast and anticipation feed into the big set-pieces and die away into hindsight. Courbet treats the chalk cliffs of Etretat as battlements; Monet transfigures them, glorifying the rock arches, making the sea caress them and drawing the sky down as infinite reassurance.

Monet brought from the seaside a lifelong preoccupation with the transforming qualities of daylight, from dazzling sunshine to doughy overcast. Here he is, indisputably, the Norman conqueror. One or two other so-called impressionists, notably Manet, may acquit themselves brilliantly on the beach while remaining, essentially, city dwellers. Renoir, as the recent selection of his landscapes at the National Gallery so woefully showed, was lost as a painter without female company.

Sisley did quite nicely in south Wales, staying at Penarth in 1897, but for him, as for the other lesser associates, impressionism was little more than a calling card and set of devices.

Along the N13 from Rouen westwards, road signs in brown on yellow advertise historic and cultural attractions. Rouen for the Monet-glorified cathedral, Honfleur, Trouville, Deauville, Dives, for impressionist-sanctified plages. From Caen onwards, D-Day takes priority. Arromanches, Bayeux. The tapestry falls in line with leftovers of the fortifications, memorialised landing grounds, military museums and cemeteries. Port-en-Bessin, Vierville, Grandcamp: place names that resound in relation to Omaha beach and Utah beach, but that are also associated with Seurat.

Seurat doesn't feature in the Royal Academy exhibition. Presumably because he wasn't a premier cru impressionist; besides which, loans would have been exceedingly difficult to secure. Yet he - and indeed D-Day, and the tapestry for that matter - are the extremities of the great intransigent narrative that extends along the Normandy coastline from the Seine estuary through to the base of the Cherbourg peninisula.

Seurat's paintings of Grandcamp and Port-en-Bessin, heady with heat haze in the summer of 1885, are impressionism rendered down into what he termed divisionism or, as we might now see it, pixellation handiwork. These resorts, composed, deserted, idyllic-looking, face seas as smooth as watered silk. No waves and, obviously, no shadow of presentiment of the epic scenes almost 60 years later when the precise layout of the coast became, for strategists, vitally important, and when the gun emplacements at Pointe du Hoc, commanding Utah and Omaha beaches, were a high point of the Atlantic Wall.

"Here in Normandy, the rescue began," Ronald Reagan declaimed in 1984, standing with his back to the sea on the cliff edge at Pointe du Hoc: land that, five years earlier, had been declared American in perpetuity. He reminded veterans of the 2nd Ranger Battalion that "in seizing the firm land at the top of these cliffs they began to seize back the continent of Europe". Half of them were killed scrambling up the 100ft cliffs only to find that the enemy had replaced gun barrels with telephone poles and hauled the guns inland to the present-day car park. A London fire brigade ladder, mounted on one of the landing craft below, lunged crazily as the Ranger manning it tried hitting the clifftop with covering fire.

Bombed, shelled, eroded over the centuries by wind and wave, part of the promontory has since collapsed. A project is under way to inject concrete into caves and fissures, and stabilise the site. Seurat's Le Bec de Hoc, a seaside Matterhorn with five seabirds flying over it, survives. It's in the National Gallery, as serene as the day it was painted.

· Impressionists by the Sea is at the Royal Academy, London W1, from July 7 to September 30. Box office: 020 7300 8000.