Dodgy French boarding house is freezing! (10)
I believe the answer is:
suspension
'is freezing' is the definition.
(freezing or suspending something)
'dodgy french boarding house' is the wordplay.
'dodgy' becomes 'sus' (suspicious).
'french boarding house' becomes 'pension' (type of boarding house in France).
'sus'+'pension'='SUSPENSION'
(Other definitions for suspension that I've seen before include "Car's shock-absorbing system" , "being taken off the job" , "Ride-smoothing system" , "Car ride smoother" , "Mixture with particles dispersed in a fluid" .)