The players ran into their dressing rooms as riot police quelled the protest, before referee Stephanie Frappart called off the game, which is the last of the season for both sides.
"The decision to permanently stop the match has been made for security reasons," she said.
Fans broke through barricades and entered the playing area at the Stade de la Beaujoire, with police initially unable to stop them before they were forced into a retreat.
Several fans appeared to target Nantes coach Vahid Halilhodzic, who was in the dug-out for the last time, having already said he would end his 33-year coaching career after the match.
Before Sunday's final league fixture, relegated Nantes had won five of their 33 league matches. Their dismal campaign left them languishing second from bottom in the standings. Toulouse are in mid-table and have nothing to play for on the final day.