Calais makes sense if the family were lace-makers:
http://www.theotherside.co.uk/tm-heritage/background/lace.htmThis would have then been an English family (high probability they were from Nottingham, also) who had come and settled in France in the early 1800s, and for some reason your William came back to England (his parents had died and he had family back there maybe?)
If you have access to an LDS center (there is one in Manchester) you could get quite a lot of info through there. They have copies of some information from the Manchester archives; the films you'd probably want to order would be:
FHL BRITISH Film
1818059, which covers:
CALAIS index to baptisms, marriages, burials, 1817-1878 Baptisms, 1817-1878; burials, 1819-1878; marriages, 1818-1872 HAVRE baptisms, marriages, burials, 1817-1863 PARIS baptisms, burials, marriages, 1784-1809
And if not there (that film is for records kept by the British of their citizens in France), then in the records kept by the French authorities (etat civil), the LDS have both the ten-year indexes and the originals. Addresses for the centers and the film catalogue are both on
www.familysearch.orgThese take a few weeks to come through so perhaps when you're going to Manchester library visit and order the films and then come back to view them when they arrive.