Noel Le Graet on Tuesday told UEFA president Michel Platini at the first meeting of the Euro 2016 steering committee in Paris that the stadiums in Lyon and Lens will both be completed "in the timeframe requested by UEFA."
Ten host cities have been selected to host the championship and the doubts over the ability to complete the development of all stadia - including the new Stade des Lumieres on the outskirts of Lyon - were discussed on Tuesday.
Le Graet told L'Equipe: "The French Football Federation is committed to deliver nine stadia, there will be nine. Today, we have 10, even if one or two are running a little behind schedule.
"Lyon has had economic problems in its financial management but it will happen. It is essential for French football and I think it will be delivered on time.
"I am very happy with the start of work. This is an important project, only from the private sector.
"St Etienne has no problem, Lille is on schedule, Nice and Bordeaux will start too, Marseille is in progress and Paris has not encountered any difficulty and neither has Toulouse."
UEFA has requested the final list of at least nine stadia to be confirmed at their next executive committee meeting on January 24 next year.
Four new stadia are being built in Lille, Lyon, Bordeaux and Nice while the grounds in Paris, Marseille, Saint Etienne, Lens and Toulouse all need upgrading.
The Stade de France in Saint-Denis is the only stadium which needs no renovation work.
The 2016 European Championships will be the third time France will host the tournament. They also held the tournament in 1984 when Platini captained the winning France team after the inaugural competition in 1960.