That pronunciation is unlikely to be French, as
Bianca isn't a French name - it's
Blanche in
France,
Blanca in Spain and
Bianca in Italy. bee-AYN-ka is the common pronunciation in English-speaking countries, but in Italy it's more like bee-UHN-ca which is I think what you're getting at. (Think how it's pronounced in the movie "10 Things I Hate About You" - that's what I mean, with the 'a' sound swallowed a bit).
:-)