Jason,

You might consider replacing the axle with an older Shimano, Sugino, Suntour or any other Japanese model of the same basic length. The tapers on the old French axles (Stronglight, TA, etc.) were similar to Campagnolo in that they typically started their taper with a smaller dimension at the ends. The Japanese axles would tend to not fit into the cranks as deeply. This normally would set the cranks too far outboard on the bike because they would not seat fully into the crank arms. However, in the case of a worn down crank arm taper this would work to your advantage, and they would likely not bottom out when tightened. This would be your least expensive route.

Unfortunately, it would be difficult to replace the bottom bracket with a more modern Japanese cartridge bearing set because the threads on your bike would still be the old metric French and incompatible with any others. So, although a Shimano UN-52 or UN-53 series would likely be readily available in most shops, and nice, and even fairly inexpensive... you do not have that option on this bike.

So, I would suggest that you simply remove the chainset and axle, then bring both the cranks AND the original axle down to a nearby bike shop. Try an older shop, one which may still have a stock of simple traditional solitary replacement axles. You could immediately test how deeply a potential new axle would fit (and without even tightening it down), comparing it to a lose fit of your original, still in hand. You will just want to be sure there is a close match to the axle lengths and that the distance between the bearing races on the axles are similar... although the adjustable cup can accommodate a bit of slack. Basic 1/4" ball bearings were standard on most any bottom brackets of the period, so this would be of little concern.

In shops where I'd worked over the years, this had proven a fast yet satisfactory fix for this issue (albeit not very profitable for the shops). The alternative would be to buy a complete new crankset.

And, PLEASE do remember that the fixed (drive side) bearing cup on the Peugeot will turn the opposite of BSC threaded cups. To remove this for any reason you will need to turn it anti-clockwise. However, if it does not seem to be excessively worn or pitted, it is probably best just left in the bike. Because of the counter-rotation of the balls, the fixed cups would sometimes tend to loosen while pedaling. A basic flaw in the French threading concept.

Good Luck!

Bob