The suspect is alleged to have called 14 different police and gendarmerie departments across the country between April 7 and May 18.
Many of his calls contained "sexual comments to female officials, sometimes insulting them," police said.
The authorities have identified a total of 34 victims.
A 47-year-old suspect was detained in a hotel in Saint-Priest near Lyon in the early hours of Wednesday.
Police said it was the first time they had been able to find the suspect who was "very unfavourably known" to them.
The man's judgment was "not impaired" and acknowledged his actions, police added after carrying out a psychiatric assessment in custody.
The suspect was due to appear before the Lyon public prosecutor's office on Friday for trial.