The most common and most likely answer to this crossword clue is the 5 letter word BREST
I've seen this crossword clue in Financial Times
B
R
E
S
T
More clues leading to the result BREST
- Source of nourishment lacking in a French port
- British taking stand in French port
- Article removed from chest in port
- City of misguided Bretons who’ve given up working?
- Leading battleships remain at French port
- Port makes bishop relax
- The emotions leaving a French port
- British remain in port
- Chicken serving one rejected in French city
- Port, or what’s left after opening of bottle
Buddy explains!

The straight part
We know that "French port" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case french port = brest.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.