Turner, 23, and Jonas, 29, previously exchanged wedding vows in a small, informal service in Las Vegas in May.
E! News said another ceremony -- filled with tears and cheers -- took place in France on Saturday.
A reception for family and friends at Château de Tourreau followed.
The couple announced their engagement in 2017.
Joe Jonas and his siblings have been out promoting the latest Jonas Brothers album, Happiness Begins.
Turner was recently seen in the X-Men movie, Dark Phoenix.