In turn, the French judge for family issues may have to rule on the case.
"Jihad" in Arabic means "effort" or "struggle", not specifically "holy war".
French law does not restrict parents' name choices for their children, provided a name does not harm the child's interests and is not opposed by other family members on reputational grounds.
The Toulouse boy called "Jihad" was born in August. Previously, other boys have been allowed to keep that name in France.
The term "jihadists" is commonly used to describe Islamist militants, such as those who carry out terror attacks in the name of so-called Islamic State (IS).
Since the start of 2015, Islamist militants have killed more than 230 people in France, where a state of emergency remains in force.
In 2013 a mother in the French city of Nimes was given a one-month suspended jail term and a €2,000 (£1,783; $2,353) fine after sending her three-year-old boy called Jihad to school in a T-shirt bearing the words "I am a bomb" and "Jihad, born on 11 September".
The sentence was for the "provocative" T-shirt, which referenced the 9/11 terror attacks in the US, but not for the name "Jihad".
In 2015 a French court prevented a couple from naming their baby girl Nutella after the hazelnut spread, ruling that it would make her a laughing stock. The judge ordered that the child be called Ella instead.
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