The incident in Vitry-sur-Seine started at around 7am (0500 GMT) when two children and five adults, including two parents, were in the school, which is being used as a leisure centre during the holidays, police said.
All children and adults except for one parent quickly left the school, a judicial source said, denying reports that any children had been briefly taken hostage.
The hostage was released safe and sound.
The 31-year-old hostage-taker, a man of African origin, lived near the school and had brandished a "convincing imitation of an automatic pistol," the judicial source said.
"The hostage was freed by the (elite police unit) RAID. Negotiations continued with the hostage-taker. He came out of the site ... and was detained by RAID police. He is uninjured," local prefect Pierre Dartout told journalists.
The judicial source said the man had "made incoherent statements and expressed a desire to die" during negotiations, adding that the hostage-taker had "at no point been threatening" with the parent who was held captive.
He tried to flee when he left the building but was caught, the source added.
RAID chief Amaury de Hauteclocque said the man "clearly had serious psychological problems and strong suicidal tendencies."
Police union representative Ludovic Magne told journalists the man asked to be "killed by police."
Around 100 people were evacuated from the neighbourhood during the hostage-taking, police said.