The incident occurred in Aubervilliers, a northern suburb of the capital, reported France Soir.
The man was armed with a sawn-off shotgun. He first took aim at his wife, who was holding a baby at the time.
A passer-by intervened and got shot himself in the arm.
Another passer-by was then hit in the neck.
The woman managed to escape, after which the man turned the gun on himself.
He shot himself in the street and died.
The two other men who were injured were taken to hospital where they are recovering.
The woman had already been identified as "in danger" from her husband. She was in the process of getting a divorce from her husband.
The local authority had given her a special mobile phone for her to use in moments of danger.
It would summon a rapid response from police. She did not have time to use the phone during Wednesday's incident.