The most common and most likely answer to this crossword clue is the 4 letter word LYON
L
Y
O
N
Buddy explains!

The straight part
We know that "French city" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case french city = lyon.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 LYON mean?
LYON noun- A big cat, Panthera leo, native to Africa, India and formerly much of Europe.
- (by extension) Any of various extant and extinct big cats, especially the mountain lion.
- A Chinese foo dog.
- An individual who shows strength and courage, attributes associated with the lion.
- A famous person regarded with interest and curiosity.
- A light brown color that resembles the fur of a lion.
- An old Scottish coin, with a lion on the obverse, worth 74 shillings.