Father in Paris eating what could be chicken spread throughout (8)
I believe the answer is:
permeate
'spread throughout' is the definition.
(I've seen this before)
'father in paris eating what could be chicken' is the wordplay.
'father in paris' becomes 'pere' ('father' in French).
'eating' is an insertion indicator.
'what could be chicken' becomes 'meat' (chicken is a type of meat).
'pere' going around 'meat' is 'PERMEATE'.
(Other definitions for permeate that I've seen before include "Soak through" , "Suffuse" , "Spread throughout" , "Spread right through" , "Flow or spread into every part of" .)