Romain Franck, who worked as a driver for the consulate, went on trial a year ago accused of exploiting reduced security checks for diplomats to smuggle 70 pistols and two automatic rifles from the Gaza Strip to the Israeli-occupied West Bank.
Travellers between the two Palestinian territories pass through Israel and are subject to Israeli security controls.
“As part of a plea bargain the defendant admitted and was convicted of three counts of importing and trading in weapons and of fraud,” the ministry said in a written response to an AFP query.
“Sentencing will be given on April 8,” it added.
He faces a possible seven-year jail term, the ministry said.
Franck was arrested in February 2018 and his trial began the following month at the district court in the southern Israeli city of Beersheba. Israeli officials have said he acted on his own without the consulate's knowledge and that diplomatic relations with France were not affected.
The Shin Bet internal security agency has said he was paid a total of around $5,500 for the guns he smuggled for a network involving several Palestinians.
At a hearing in November Franck's lawyer, Kenneth Mann, said that his client's actions were not those of someone seeking to help Palestinian militants in their battle with Israel.
“He was scared, he is young and inexperienced,” Mann told reporters. “He has no ideological or political involvement in the Israeli-Palestinian conflict.”