Baup, who took charge of Marseille in 2012, led the side to a runners-up finish in Ligue 1 last season at the expense of champions Paris Saint-Germain.
Despite his future remaining uncertain, Labrune insists that Baup will remain at Stade Velodrome for an extra year.
"Elie has adapted perfectly. Sometimes it feels like he has been at the club 10 years," Labrune told L'Equipe.
"He is so efficient and competent that we have decided to prolong his contract for one more season."
Baup has previously managed Saint-Etienne, Bordeaux, Toulouse and Nantes.