My ex husband filed false contempt of court charges against me is there any legal action I can take?

Not enough information.  You do not indicate what is in court in which state, where he filed, why the charges are "false," or anything else that would allow a meaningful response.  Your best bet is to set a consultation appointment with this office, or that of another family law specialist, preferably in whatever State the contempt charge is pending, along with all relevant papers, court filings, and proof of relating to whatever the issue actually is.