The problem is that creating a Franco-British rivalry 'throughout history' would require creating a unified 'France' a lot earlier than happened OTL. Remember, that between the Late Middle Ages and the Age of Nationalism, the King of France was mostly a figurehead, and really it was the autonomous duchies such as Normandy, Aquitaine, and Burgundy that held the real power.
Maybe the POD could be that William the Bastard's invasion of England could fail. That would reduce the power of Normandy which could in turn allow France to unify under Aquitaine (Normandy's great rival). Really, it was the Anglo-Norman Union which prevented the centralization of France as the personal union with England gave Normandy way too much power to ignore the authority of the French King.
But I still don't see how an earlier unified France could result in a Franco-British rivalry, as any alliance of Britain and Germany could squash France no problem: it was really only the Anglo-Germany rivalry which allowed Unified France to grow in power as it played the allies off against each other. After all, how could France have ever secured the Low Countries if it hadn't been for Britain supporting their occupation to keep Antwerp out of German hands??
If anything my suggested POD of William the Bastard failing in his invasion of England would result in a weaker, less unified England, so maybe we would see an earlier unified France facing off against Germany with no united Britain at all. That certainly seems more plausible to me than a France vs. Britain standoff.