The lawyer for Pengo Bossio Wangi, the one person killed during the attack, told French media the move to place the suspect under observation was "very rare".
He alleged that it was being used to portray the suspect as criminally irresponsible rather than having acted deliberately.
Wangi, a 26-year-old French-Congolese martial artist, was named as the one fatality on Saturday.
The mixed martial arts club where he trained paid tribute to him, saying: "On the mats as off them, he was one of those who lead by example: present, respectful, always ready to lift others up.
"His smile, his energy and his generosity will remain etched in our walls and in our hearts."
Three of those injured in the attack were taken to hospital in a serious condition - including a 12-year-old girl who remains in a critical condition.
The mayor of La Verrière, Nicolas Dainville, told French radio network France Info on Sunday that he had spoken to the girl's mother over the phone and confirmed she was "doing better".
Another injured resident was recovering while a third remained in a critical condition, he said.
The suspect had been known to police prior to the attack but not to France's intelligence services, local media report. PNAT previously said he had four previous convictions that had been "automatically expunged".
He is thought to have used an old semi-automatic weapon during the attack, firing in bursts from his car window.