Mission in Paris that served travellers principally (5)
I believe the answer is:
quest
'mission' is the definition.
(a quest is a mission or search)
'in paris that served travellers principally' is the wordplay.
'in paris that' becomes 'que' (French for 'that').
'principally' says to take the initial letters.
The first letters of 'served travellers' is 'st'.
'que'+'st'='QUEST'
(Other definitions for quest that I've seen before include "Prolonged search" , "Long or arduous search" , "A search or hunt" , "Mission" , "Pursuit" .)