Deleted member 94680
True, which is why I said reasonable chance instead of a higher probability. Having thought about it a bit more an incident like: the sinking of USS Maine; or the Russian fleet that would eventually be annihilated at Tsushima attacking British trawlers in the North Sea because they mistook the fishing boats for enemy destroyers; would be required. That is the Royal Navy sinks a French warship having mistook it for a German ship and that whips up French public opinion sufficiently to force the French Government into war against its better judgement (which as you wrote was to stay on the side lines and watch the two combatants weaken themselves).
Except when that happened it didn't lead to war? https://en.wikipedia.org/wiki/Dogger_Bank_incident There was a lot of sabre-rattling and protests, but a International Conference of Inquiry settled the issue rather than force.
Would this be a case of tempers are already inflamed in Britain due to the War with Germany and therefore they mistake a French warship for a German one (not sure how that would happen, tbh) and sink it for jollies? If it was an accident, I'm pretty sure Britain - already fighting Germany - would go all-out diplomatically to placate France to avoid the possibility of a French DoW.