The 18-year-old was sent back to France on Thursday following a demand from French authorities, the department said.
He had been arrested on May 14th.
The Tribune de Genève newspaper said the teenager left Geneva on May 12th for Istanbul in a second attempt to go on to Syria.
The following day, France issued an international warrant for his arrest.
He was sent back to Switzerland on May 14th and arrested.
He had tried to travel to Syria in March but was stopped in Munich in Germany as he was still a minor.
The young man's mother told the Tribune de Genève that he had changed completely in the span of three months and became radicalized after the January jihadist attacks in Paris that killed 17 people.
“He said he could not practice his religion peacefully in France, he used words that were not his, he was under a spell,” said his mother, a teacher from northern France.
The Paris attacks led to a series of anti-terrorism laws coming into effect in France aimed at stopping people from travelling out of the country if they are suspected of trying to join jihadist groups.
Some 1,400 people living in France have either joined the jihadist cause in Syria and Iraq or are planning to do so, Prime Minister Manuel Valls said in March.