An enormous hit in its day and writer/director Claude Lelouch's best known film, one can't help but see A Man And A Woman now as a basically an Elvis Presley movie passed through French art-house sensibilities. Which is to say that although Jean-Louis Trintignant as the Elvis character (a racing car driver) and Anouk Aimée (a script girl) do not sing or dance (although there is one musical number), are refined rather than rambunctious, and eat Chateaubriand rather than hamburgers, there are lots of extended scenes that mark time to the accompaniment of swinging French lounge/pop music, not least of which is the famous theme tune, courtesy of Francis Lai.
In every respect this is of course much better cinematic quality than anything any Hollywood studio hack knocked off and has a well-written script and a judiciously light directorial touch, giving it appeal to a civilized middle class audience looking for a tasteful romantic interlude as opposed to a bit of necking at the drive-in. At the end of the day however, there is not a whole lot to differentiate between this and Viva Las Vegas (1964) except as Trinitagnant says, this is "serieux" cinema.
The film won Best Foreign Film and Best Original Screenplay Oscars and La Grand Prix at Cannes. Lelouch revisited the lovers in a sequel A Man And A Woman: 20 Years Later which was by all accounts an unmitigated disaster.