Images and footage from Thursday’s demonstrations, captured by TV channel BFM, shows the police officer hitting a man on the ground between the legs, and then leaving.
The man is seen holding a camera.
Lawyer Lucie Simon said she was filing a complaint on behalf of her client, a 26-year-old Franco-Spanish engineer who was taking pictures of the gathering, for “voluntary violence that led to mutilation by a person vested with public authority”.
“It was such a strong blow that he had to have a testicle amputated,” she said, adding that the engineer was still in hospital.
“This is not a case of self-defence or necessity. The proof is in the images we have and the fact that he was then not arrested.”
The engineer, who lives on the French Caribbean island of Guadeloupe, “is still in shock and keeps asking why” he was wounded, the lawyer added.
The Paris police department said it had ordered an internal investigation, adding that the incident had happened in “a context of extreme violence and within a police manoeuvre to arrest violent individuals”.
Government spokesman Olivier Véran told the BFMTV broadcaster that he felt “empathy” for the young man.
But he stressed “the need to understand the conditions in which this intervention occurred”.
The interior ministry said 80,000 people marched in Paris on Thursday, as part of nationwide protests against President Emmanuel Macron’s plan to extend the retirement age from 62 to 64.
The hard-left CGT union however said it counted 400,000 protesters in the French capital.
The demonstration was largely peaceful, but around the Bastille area of Paris, some demonstrators hurled bottles, bins and smoke grenades at police, who responded with tear gas and charged to disperse the troublemakers, according to AFP journalists at the scene.