If a person filed a kidnapping charge against someone and the charge was false,
And the person who filed the charge had no criminal record, would filing the false charge be considered a felony or misdemeanor?

First it would have to be considered a false report. Then the DA will have to decide it was done on purpose and they will have to decide to file charges ( this seldom happens)

It will depend on the facts of the case.
Filing a False Police Report: Penalties and Consequences (http://criminal-law.freeadvice.com/criminal-law/white_collar_crimes/false-police-report.htm)