France can, with some justification, claim to have invented the whole concept of cinema. Film historians call The Arrival of a Train at La Ciotat Station, the 50-second film by the Lumière brothers first screened in 1895, the birth of the medium.

But the best-known early pioneer, who made films with some kind of cherishable narrative value, was Georges Méliès, whose 1902 short A Trip to the Moon is generally heralded as the first science-fiction film, and a landmark in cinematic special effects. Meanwhile, Alice Guy-Blaché, Léon Gaumont's one-time secretary, is largely forgotten now, but with films such as L'enfant de la barricade trails the status of being the first female film-maker.

The towering achievement of French cinema in the silent era was undoubtedly Abel Gance's six-hour biopic of Napoleon (1927), which like many large-scale productions of the time, has had a choppy subsequent history. Thanks largely to the efforts of film historian Kevin Brownlow, a 330-minute restored version – complete with the original's three-projector finale – can be occasionally seen; but since Gance originally planned a six-film cycle, of which only number one was ever completed, we will only ever have a fraction of what was intended. But Belgian-born Jacques Feyder was not to be outdone, with the extraordinary L'Atlantide (1921), and Faces of Children (1925). And the artistic ferment of pre- and post-first world war France made itself felt cinematically, with an amazing outpouring of avant-garde short films. Key titles include Jean Vigo's Soviet-influenced A Propos de Nice (1929), Fernand Léger's Dada-ist Ballet Mecanique (1924), and two surrealist masterworks: Germaine Dulac's The Seashell and the Clergyman (1928), with an Antonin Artaud screenplay, and the Buñuel/Dali collaboration Un Chien Andalou (1929).

The early sound years saw an explosion of talent. Playwright Marcel Pagnol put adaptations of his celebrated Marseilles plays into production – first Marius (1931), then Fanny (1932), and finally César (1936), which he directed himself. René Clair made the musical, Under the Roofs of Paris (1930). But the period really belonged to the pioneers of "poetic realism" – Vigo, Jean Renoir, Julien Duvivier and Marcel Carné. Masterpieces abounded in the interwar period: Vigo's scabrous satire Zero de Conduite (1933) was followed by the lyrical L'Atalante (1934). Tragically, it was his last film, as he succumbed to tuberculosis the same year, aged just 29. Renoir's career took off with Boudu Saved from Drowning (1932), and thereafter produced a string of brilliant films up to the outbreak of the second world war: A Day in the Country (1936), The Crime of Monsieur Lange (1936), La Grande Illusion (1937), La Bête Humaine (1938), and arguably the greatest of all: La Règle du Jeu (1939). Duvivier weighed in with the Algeria-set gangster yarn Pépé le Moko (1937), while Carné also anticipated American-style noir with Quai des Brumes (1938) and Le Jour se Lève (1939). But Carné, arguably, outdid them all with Les Enfants du Paradis (1945); filmed during the Nazi occupation, the romantic melodrama set in the 19th-century theatre world became a symbol of national cultural identity when it was finally released.

The disruption caused by the war saw the avant garde regain the upper hand, with Robert Bresson's minimalist Diary of a Country Priest (1951) and Jean Cocteau's La Belle et la Bête (1946) and Orphée (1950). (Fans of The Matrix might notice where they borrowed their liquid-mirror idea from.) Cocteau's work also gave a chance to a new generation in the shape of Jean-Pierre Melville, who was hired to direct an adaptation of Les Enfants Terribles (1950). Perhaps not coincidentally, a new generation of politically radical film critics were growing up, mentored by André Bazin at Cahiers du Cinema. Their work fed directly into the explosive success of the French New Wave in the late 1950s: critics such as François Truffaut, Jean-Luc Godard and Claude Chabrol transferred their ideas directly to the screen. Truffaut's The 400 Blows (1959) and Godard's Breathless (1960) were the vanguard, but the New Wave triggered a decade and a half of brilliance, with a profusion of brilliant film-makers associated with the movement – Alain Resnais, Agnès Varda, Jacques Demy, Louis Malle, Eric Rohmer. Meanwhile Melville, who had prospered in the New Wave era, completed a trilogy of masterworks at the end of the decade: Le Samourai (1968), Army in the Shadows (1969), and Le Cercle Rouge (1970).

After leaving its mark on a myriad of European national cinemas, and finally Hollywood by the end of 1960s, the French New Wave began to finally peter out; but coming up behind were a group of surface-obsessed style merchants who established the glossy 1980s "cinema du look". Jean-Jacques Beneix, with Diva (1981) and Betty Blue (1986), Luc Besson with Subway (1985), and Leos Carax with Mauvais Sang (1986) were the key figures here, much given to the speeding motorbike, the studied gesture and the highly coloured set-piece.

Realism made a comeback in the 1990s, primarily through the Mathieu Kassovitz-directed La Haine, but the leading influence of the subsequent generation has undoubtedly been Jean-Pierre Jeunet who, with Delicatessen (1991) and Amélie (2001) perfected a Gallic answer to the comic-book-influenced style of Sam Raimi, Terry Gilliam and Barry Sonnenfeld. In recent years, Jacques Audiard has, arguably, become France's most respected auteur, with The Beat That My Heart Skipped (2005) and A Prophet (2010).