The most common and most likely answer to this crossword clue is the 5 letter word DUMAS
I've seen this crossword clue in The Sunday Telegraph
D
U
M
A
S
Buddy explains!

The straight part
We know that "French author" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case french author = dumas.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.
What does DUMAS mean?
DUMAS noun- A Russian legislative assembly such as the historical duma of the Russian Empire or the modern lower house of the Federal Assembly (the Russian national parliament).
- A drink mixing wine and vodka.