Long-term visa: Process after you arrive in France (Paris)

Since early last year I have kept an apartment in Paris and traveled back and forth between Paris, Houston and Cancun. As I was pushing the limit for the number of days I could stay as a tourist in Europe, I applied and received a long-term visa for France.

So my question is what happens next? I understand I am supposed to fill out a form and submit it but then what? I think I read somewhere that I might be called in for an physical exam? Does anyone know how soon after I submit the form I might be called in? Since I travel between Paris and the Americas my concern is that I might be out of the country when I am asked to come in.

Thanks for any help!

-James