Lodging of a false FIR/complaint is punishable under IPC. Such complainant can be proceeded against under Indian Penal Code section 211 False charge of offense made with intent to injure by the police. A private person against whom a false FIR has been lodged can also file a complaint in court for the offense of defamation.
Since the complainant of the FIR is your wife, it is wise to resolve the dispute on amicable grounds, rather than taking it into the courts. Which would be time-consuming and might have adverse effects on the work visa/permit that you have mentioned.