It's not just French/Britain. The book "How music works" describes how each country and, hell, cities, had different tunings, so an Italian singer with a perfect pitch visiting Germany cannot really perform. Maybe just the local organ builder had a different tuning fork when building the church and everyone tuned from there :)
Similar to how people didn't have standard time until relatively recently and the one clock at the town square can be off by quite a bit with the next town.
But from what I've read the British actually tried to adopt the French standard and made some conversion error, they didn't come up with their own thing independently.
Similar to how people didn't have standard time until relatively recently and the one clock at the town square can be off by quite a bit with the next town.