Do you know "Quartet for flute, oboe, clarinet and piano" by the 20th century French composer Damase? It is a very French and elegant piece. The link is for the second movement, but Damase has many other enjoyable second movements.
Damase was a pupil of Cortot and the first to record the complete works of Fauré's Nocturnes and Barcaroles.
Because it was composed as a neoclassical piece, it was not highly acclaimed in the 20th century, but it has been gaining popularity recently and recordings are becoming available. It's very French. If you like Poulenc, you'll probably like Damase too.