Upgrading my french PX-10e with shimano 105 cranks. What bottom bracket can I use with this 68mm bottom bracket with french threading? Is there a threadless BB available?
Velo-Orange makes threadless BB's and French threaded BB's under their Grand Cru line. There is always also Phil Wood if you're rolling in money. They are all JIS (square) tapered. Some other companies (like Stronglight) have also made threadless bb's (for frames which typically have had their threads ruined) in the past - I don't know if this is current.
I'm not entirely sure what BB-6700 has to do with this, though.
I think I see why BB-6700 may be there - you're trying to get a hollowtech/octalink/some other type of setup going. As far as I know, nobody makes a product which will allow you to do this.
Shimano does still make new cranksets which are JIS tapered in the Sora line, but if you want something fancier, you'll have to go with an older used crankset. You can always get nice new replacement chainrings if they're a bit worn.
Edit: Just saw the outboard bottom bracket page from Phil Wood. Its expensive, but I think it may work depending on the crankset you want to use.