The most common and most likely answer to this crossword clue is the 6 letter word RACINE
I've seen this crossword clue in The Daily Telegraph
R
A
C
I
N
E
More clues leading to the result RACINE
- Clubs to break old rule for French writer
- Nation embraces popular French playwright
- People defending popular dramatist
- Hurry to engage trendy French dramatist
- French writer‘s home flooded by water channel
- French dramatist elected to enter competition
- Playmaker competin’ with energy
- Dramatist in France briefly flying east
Buddy explains!

The straight part
We know that "French dramatist" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case french dramatist = racine.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.