My sense is that they won't.
The French believe they should be the world's leaders (no kidding, they really do) and they're going to be a pain in our ass in perpetuity.
By the way, I am not convienced that the French "Speaking" people in Europe (I'm leaving Belgium after 4.5 years in Europe this month) like anyone other than themselves, but are very happy to Bash American's in EUropean Company and other EUropeans when amongst themselves (The French love only themselves and dislike or hate everyone else). Just my take after putting up with their Anti-Americanism personally.
The radical Islamic Front should now realize that expanding the war against America was not a smart strategic thing to do. Unlike present day Western Europe, we fight back. The radical islamic terrorist have suffered major losses in Afghanistan and Iraq. Both places were viewed as strongholds for radical anti-american sentiment (Baathist and Taliban). This will force the terrorists to redirect their efforts at Western Europe and Russia. Eastern Europe (Poland, etc.) has also demonstrated the will to fight back. If radical islamic terrorists have gotten WMD from Iraq, expect them to deploy these weapons against Russia and Western Europe. If they use them on the US or England, losing Afghanistan and Iraq will pale in significance when the US and its coalition forces step it up a notch. In other words, it will take a 911 event within France to shock their populace and wake them to the current ongoing islamic invasion of Europe. Wonder what Charles Martel did to rally his troops ?