My soon to be ex-wife entered into our marriage for the purpose of
gaining American citizenship, we have one child and we reside in
America.  How can I have my spouse deported back to France?

What is her current status?  Does she have a green card?  If she has
no green card, the divorce should put her out of status.

Be advised that any accusations made at your spouse regarding
fraudulent behavior may also implicate you in the eyes of the INS.  Of
course, seek a licensed immigration attorney for legal advice.