The boys – aged 14, 17 and 18 – were expelled after months of debate about whether an under-turban, or keski, was acceptable under the new law.
The boys had been taught separately since returning to school in September.
They are the first Sikhs punished by the new law, although several Muslim girls have already been expelled.
The judgement was seen as a challenge to the French secularity law banning “conspicuous” religious items in the classroom.
“I have a feeling that the decision had already been taken,” said Felix de Bolloy, the boy’s lawyer, outside the school.
One of the boys, Ranjit Singh told the AFP news agency: “We’ve been stuck in the cafeteria with photocopies of the course work since September.
“We’ve fallen significantly behind with our school work, and want to remain in the public educational system.”
The French secularity law, primarily aimed at stemming the growing numbers of Muslim girls wearing headscarves in school, came into force at the beginning of September.
It prohibits the wearing of religious symbols and also banned Christian crosses and Jewish skullcaps.
The law also outlawed the Sikh turban, although French authorities have admitted they did not consider the Sikh community when the law was being drawn up.
Sikh males are required by religion to allow their hair to grow, and most wear a turban to keep the growth under control.
In most French schools Sikhs have reached a compromise that has allowed them to wear the keski, a smaller version of the turban, to control their hair.
However, the three boys, who attended the Elysee Louise Michel in Bobigny, north-east of Paris, found themselves segregated from other students when they returned for the new school year in September.
They were finally expelled on Friday, but Mr de Belloy said he plans to appeal.
In a separate case, four Muslim girls were expelled from their school in the eastern region of Alsace for wearing headscarves.
At least a dozen other girls have been expelled from schools across France.