Residence in outskirts of third-rate French city (7)

I believe the answer is:
tenancy
'residence' is the definition.
(tenancy is a kind of residence)
'outskirts of third-rate french city' is the wordplay.
'outskirts of third rate' becomes 'te' (I can't explain this - if you can you should believe this answer much more).
'french city' becomes 'Nancy' (city in France).
'te'+'nancy'='TENANCY'
'in' acts as a link.
Can you help me to learn more?
(Other definitions for tenancy that I've seen before include "Let" , "Rental arrangement" , "Lease (of a house)" , "Period occupying house" , "Rental agreement" .)
