The most common and most likely answer to this crossword clue is the 4 letter word FLIC
I've seen this crossword clue in The Guardian
F
L
I
C
More clues leading to the result FLIC
Buddy explains!

The straight part
We know that "busy in France" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case busy in france = flic.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 FLIC mean?
FLIC noun- A data file containing computer animations.
- A French policeman.