Almost see Frenchman being calm (6)
I believe the answer is:
serene
'being calm' is the definition.
(synonyms)
'almost see frenchman' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'frenchman' becomes 'rene' (common French name).
'see' with its final letter taken off is 'se'.
'se'+'rene'='SERENE'
(Other definitions for serene that I've seen before include "Calm and unruffled, like a princely title." , "without any trouble" , "Calm, untroubled" , "Tranquil, unruffled" , "Calm and unclouded" .)