French-thread bottom bracket cups use 35 mm x 1mm threads. They are getting hard to find. If you have a French bicycle with sound bottom bracket cups, you may want to re-use them, even if you wind up changing the axle. Since French bottom brackets are normally the usual 68 mm width, British/I.S.O. bottom bracket axles will sometimes work.
French bottom bracket cups usually have thinner walls than Japanese ones, so the bearing ridges on the spindles are farther apart. If you use a standard Japanese spindle, the adjustable cup won't be able to screw in far enough to snug up the bearings, or if it does, it will sink into the bottom bracket shell so that you won't be able to install the lockring.
The good news is that a Japanese spindle made for an Italian size (70 mm) bottom bracket will usually fit! In the J.I.S. marking system, these are the spindles that are marked with a "5" code. Spindles for 68 mm bbs have codes beginning with 3. This trick often makes it possible to upgrade an older bike from cottered to cotterless cranks, at a reasonable cost, or replace a worn French cotterless spindle that is no longer available -- but see warning below about French crank extractors.
Few cartridge bottom brackets are available in French thread, but Phil Wood retaining rings are available in French size. They work with Phil Wood bottom brackets and Shimano UN72 units. Velo Orange makes a French-threaded bottom bracket.
French-thread bottom brackets, like Italian, use regular right threading on both sides. This means that the fixed cup will have a tendency to loosen up in use. The best prevention is to make sure it is really tight. In some cases, a thread adhesive may even be called for.
Some French bicycles, notably many Motobécane models, used Swiss thread bottom brackets. These have the same thread and diameter as French, but use a left thread for the fixed cup. This makes life interesting when you need to remove the fixed cup and don't know which way to turn it. Good luck. Phil Wood offers Swiss retaining rings, and Velo Orange makes a cartridge bottom bracket which uses expanding sleeves instead of threads, and also will work in a French-threaded frame.
Newer French bicycles commonly use Italian or British/I.S.O. bottom brackets.