Oliveira crashed on the opening lap of the Spanish Grand Prix at Jerez on Sunday, the Portuguese taken out by Yamaha's Fabio Quartararo and dislocating his left shoulder.
Malaysia-based RNF Racing said doctors had repositioned the shoulder at the time but further assessments revealed a more severe injury.
"Although Oliveira and his doctors have decided against surgery, he will need to focus on the healing process and will not be able to participate in the French round," they said in a statement.
It will be the second time this season that Oliveira has missed a race after being downed by another rider.
He was also taken out by Honda's Marc Marquez in the Portuguese season-opener and missed the following round in Argentina.
Savadori took part in the official MotoGP test with RNF at Jerez last Monday.
