Forward Dembele faces about six weeks on the sidelines with an injured left hamstring, while winger Doue will be out for around four weeks due to a calf problem after they picked up the injuries during a 2-0 win over Ukraine in Poland.
European champions PSG said on Sunday that they had called for a "more transparent and collaborative medical-sporting coordination protocol between clubs and the national team" in a letter to the French Football Federation.
"(PSG) had sent the federation concrete medical information, even before the French national team began training, on the acceptable workload and injury risks for its players," the club said in a statement.
"The club regrets that these medical recommendations were not taken into account by the French national team's medical staff and that there was a total lack of consultation with its medical teams."
PSG said exchanges between clubs and France's medical staff should be documented, and a "precautionary principle" should be followed when selecting players for national duty, particularly when they are undergoing treatment for a medical condition.
"The recent serious and avoidable events must give rise to rapid and immediate corrective measures," they added.
France coach Didier Deschamps defended his decision to field Dembele on Friday, saying the forward was fit despite being substituted during a Ligue 1 game at Toulouse on August 30th following a right hamstring issue.
"I was sure that he was capable of playing a high-level match; otherwise, I would not have played him. This time, it's the other thigh," Deschamps said.
"He was fit. It is unfortunate for him, but it could have happened to another player."