The French port is heavy (6)
I believe the answer is:
leaden
'heavy' is the definition.
(I know that heavy can be written as leaden)
'the french port' is the wordplay.
'the french' becomes 'le' ('the' in French).
'port' becomes 'Aden' (port in Yemen).
'le'+'aden'='LEADEN'
'is' is the link.
(Other definitions for leaden that I've seen before include "Depressing - heavy" , "Heavy and slow, as if weighted down with heavy metal" , "Leaned over in slow, heavy way" , "Dull, heavy, slow" , "Describes grey overcast skies" .)