For American painters drawn to Paris by the avant-garde, it was not an easy time. In France they were considered neophytes; in the United States they were regarded as heretics. Many French artists wondered why American painters bothered to come to France at all. Seen from Paris, New York in the interwar years seemed a far more exciting place.

But there were still many Americans eager to travel to Paris to discover life after figurative art, and these explorers are the focus of an unusual exhibition at the Musée d'Art Américain Giverny, the elegant small museum owned by the Terra Foundation for the Arts, of Chicago, near Monet's Normandy home. The show, ''A Trans-Atlantic Avant-Garde: American Artists in Paris 1918-1939,'' is here through Nov. 30 and will then travel to the Tacoma Museum of Art in Washington (Dec. 18 to March 28) and to the Terra Museum of American Art, Chicago (April 17 to June 27).

What these artists were after was novelty. Several had tried post-Impressionism and Fauvism, but they realized something more daring was afoot in Paris when they encountered Cubism at the landmark show at the Armory in New York in 1913. Once World War I ended they jumped at the chance to break free from what they considered the smothering conservatism of American art. ''When will you give to your artists the opportunity that you have already given to scientists and engineers?'' John Storrs, a sculptor en route to Paris, asked New Yorkers in an article in The Little Review in 1922.

Still, the Giverny show remains somewhat anthropological, because few of the 30 American artists represented became household names. True, there are photographs by Edward Steichen, Berenice Abbott and Lee Miller, although Man Ray and Alexander Calder were the only Americans who were truly integrated into the Paris art scene. Most spent a few years learning the new art, then returned home.

In the show are eight European artists based in Paris who influenced the Americans, not least Marcel Duchamp, who first wooed Man Ray to Paris in 1921, and Fernand Léger, who encouraged several of the expatriate artists and who was himself fascinated by the United States long before he paid his first visit to New York in 1931.

The exhibition is in four sections, with the first, ''The Purity of the Object,'' dominated by the spirit of Léger's post-Cubism. In it, Stuart Davis and Charles Demuth interpret Paris scenes in a Cubist manner. Patrick Henry Bruce went further toward abstraction, painting still lifes of multicolored cylinders, triangles and other shapes while eliminating perspective.

Gerald Murphy was the wealthy man-about-Paris who inspired the character of Dick Diver in F. Scott Fitzgerald's ''Tender Is the Night.'' He turned to painting when he discovered Picasso, Braque and Gris. Then, after the Wall Street crash, he returned to New York. Only eight of his works are known to have survived, but his graphic images of consumer culture, like ''Razor,'' set the stage for Pop Art four decades later.

The next section, ''The Birth of Geometric Abstraction,'' reflects the influence of the Paris-based Dutchman Piet Mondrian on a number of Americans, including Albert Eugene Gallatin. Gallatin was also a collector and played an important role in introducing avant-garde art to the United States when he opened the Gallery of Living Art at New York University in 1927.

Mondrian's geometric color scheme also inspired Calder. ''When Calder met him in 1930, he said, 'Wouldn't it be better if the colors moved?' '' recounted Sophie Lévy, chief curator of the Giverny museum, who organized this show. ''And that's how he began his mobiles. At first, they were three-dimensional collages turned by a motor. Then they evoked planets and the universe.'' In this, Calder was also influenced by Miró, Brancusi and Jean Arp.

The section dealing with Surrealism, ''The 'Chemists of Mystery,' '' is inevitably dominated by Man Ray, who found himself designated the Surrealists' photographer by the movement's leader, André Breton. Man Ray's own contribution to Surrealism came through his experiments with hyperexposure and rayographs, a technique that he developed with Miller.

The show's final section, ''The Portraits of the Avant-Garde,'' again features Man Ray, whose principal job, in Breton's view, was to photograph artists of whom he approved, among them Duchamp, Ernst, Dalí, Brancusi, Miller, James Joyce and Breton himself. Appropriately, Man Ray's portrait of Gertrude Stein is on display: it was at the writer's salons that visiting American artists hoped to make the right connections.

Abbott's portraits are also well represented here. She, too, photographed Joyce as well as Sylvia Beach, whose bookstore, Shakespeare & Company, was a gathering point for expatriate writers; Janet Flanner, the longtime Paris correspondent of The New Yorker; and the aged Eugène Atget, the French photographer who most influenced Abbott. Abbott herself appears in a portrait by Man Ray.

When they returned to the United States, many of these artists sought to propagate ideas they had gathered in Paris, but few were heralded as innovators. Rather, it was through exhibitions of works by European artists like Picasso, Matisse, Léger, Brancusi and Duchamp that New Yorkers were won over to Modern art. During World War II, with Breton himself an exile, New York even became the temporary capital of Surrealism.

Finally, after the war an authentically American avant-garde arrived with Jackson Pollock and the birth of Abstract Expressionism. As for many of the American artists who had gone to Paris to learn the French way, well, they were largely forgotten until the American museum in Giverny rediscovered them this month.

Photos: Stuart Davis's ''New York-Paris No. 1,'' above, and Man Ray's ''Kiki,'' both from ''A Trans-Atlantic Avant-Garde: American Artists in Paris 1918-1939.'' (Photo by University of Iowa Museum of Art); (Photo by Man Ray Trust)