Kylian Mbappe said last month he would not play in the tournament following his move to Real Madrid, with clubs not required to release players for the Olympic Games.
Antoine Griezmann had also expressed an interest at one point but Henry knew the likelihood of being able to call upon some of France's star names was slim.
Paris Saint-Germain duo Warren Zaire-Emery and Bradley Barcola, who are also in the France squad at Euro 2024, were named by Henry in a preliminary list in June but will not take part either.
Lyon attacker Rayan Cherki and Rennes striker Arnaud Kalimuendo were selected along with Crystal Palace forward Jean-Philippe Mateta, who is one of the three permitted players aged over 23 in the squad.
France play the United States in their opening game on July 24 in Marseille. They will also face Guinea and New Zealand in Group A.
