Your bottom bracket spindle may not be the correct length or taper for your crankset. Have you measured the spindle? Both for overall length and symmetry? You can look up what length is required for your crankset and compare.

Taper (ISO vs. JIS) is probably correct ...if the previous owner didn't install a mismatched spindle/crankset combo. Campagnolo cranksets are ISO. Most others, particularly from Asian manufacturers, are JIS.

And instead of judging your crankset/spindle compatibility by chain stay clearance, you may want to consider measuring chainline instead. Stay clearance varies from bike to bike. Chainline is pretty much standardized, and directly affects whether your derailleur can reach your inner and outer chainrings. Chainline for a road double should be about 43.5 mm, measured from the frame's centerline to the midpoint between your chainrings.

A Bianchi's not going to have a French bottom bracket, even if it was sold in France. It'll be either Italian or English, largely depending on where the frame was built. If it's an Italian frame, there's a pretty good chance the bottom bracket will have Italian threading. If the frame was contract-built in Asia, the bottom bracket will almost certainly be English threaded.

If the existing bottom bracket isn't a cartridge, you may find threading markings on the cups, which will identify what you've got:

1.370" or 1.375" diameter, 24 threads per inch, 68 mm shell width = English
35 mm diameter, 1 mm thread pitch, 68 mm shell width = French (or Swiss)
36 mm diameter, 24 threads per inch, 70 mm shell width = Italian

Not every crankset is designed to use the same spindle length. Even cranksets from the same manufacturer and era may require different spindles. It varies from model to model. That's why there are dozens, maybe even hundreds, of different spindle configurations. (Yellow Jersey lists a bunch of 'em.)