Attributing all this to intelligence sharing alone seems an oversimplification. I suspect the difference in the level of assimilation between British Muslims and their French counterparts is the biggest factor.
I've traveled between London and Paris frequently. I found the visibility of fundamentalist muslims in the UK to be much higher than anywhere in France. The burka and niqab, for example, is not only illegal but even before being so it was extremely unpopular in France (I believe the estimate was ~200 for the entire country). Yet, walking around London and it's outskirts this was a common sight. France has managed to…
Yet any extremist can literally walk into France and terrorize, which is essentially what's happened.
So perhaps the biggest difference the fact that Britain has a physical border wall?