Jean Dujardin was born and raised in Rueil-Malmaison, France, outside Paris.
Every search I attempted in trying to find any ounce of information on Dujardin's religion came up empty. Aside from the fact that he said, "My God" more times than I could count when he won best actor at the Screen Actors Guild Awards, there's not a shred of anything.
There are a lot of Catholics in France, but I have no reason to believe Dujardin joins them. Most likely he joins the significant number (35%) of non-religious folks, who occasionally say "My God" because they haven't found any secular words that are quite as satisfying.
As far as I can tell, Dujardin doesn't have much to say about politics. If I spoke French, I might have a different story for you, but alas, I was left to looking at bad Google translations of web pages.
With that said, it looks like the French press generally assumes that Dujardin leans to the left politically. French president François Hollande, a member of the Socialist Party, was apparently trying to court the popular actor in 2012 during his campaign for the presidency, but he wasn't able to get an official endorsement from Dujardin.
That's all I was able to find on Dujardin, but if you speak French and you know anything else about his religion or politics, let us know in the comments!