Building a number meet collapsed, trapping Frenchman, finally (8)
I believe the answer is:
tenement
'building' is the definition.
(tenement is a kind of building)
'a number meet collapsed trapping frenchman finally' is the wordplay.
'a number' becomes 'ten' (ten is a kind of number**).
'collapsed' indicates anagramming the letters.
'trapping' indicates putting letters inside.
'finally' suggests the final letters.
The final letter of 'frenchman' is 'n'.
'meet' anagrammed gives 'emet'.
'emet' going around 'n' is 'ement'.
'ten'+'ement'='TENEMENT'
(Other definitions for tenement that I've seen before include "Building divided into small let units" , "Apartment in a US block" , "slum housing?" , "Old dwelling for multiple occupation" , "Piece of owned land" .)