First, the new BB probably won't cost that much for the Stronglight crankset ... just ASK whoever is selling the crank how much a compatible bottom bracket will cost ... t/he/y must also be selling a BB, particularly if it is a dealer.
You can get an OLDER 5-arm 110BCD Shimano XT/LX crankset from the early 90s ... on eBay if you are patient.