Renault not ready for podium – Alonso
The Spaniard ultimately finished the race just eighth, lamenting that his Renault did not deliver good enough race pace.
"On Saturday and before the race we were optimistic, but we need to be realistic," he told Telecinco.
"We are really only fighting in the middle of the grid."
Some analysts surmised that the 26-year-old former double world champion's race strategy simply failed.
But Alonso explained: "If you are slow and you can't get into a rhythm, your strategy doesn't matter."
His countryman Marc Gene, a test driver for Ferrari, agreed that Alonso's unfulfilled potential was the "negative surprise" of the French grand prix.
"We expected much more from him," Gene wrote in the Spanish newspaper El Mundo. "Even at Ferrari we thought he was going to be our competitor."
The German newspaper FAZ reports that Alonso is growing impatient with Renault, and that the feeling may also be mutual by many inside the French squad's pits.
One engineer is quoted as saying: "Fernando thinks only about Fernando. (In Canada) he wasn't even at the after-race briefing."
Engineering chief Pat Symonds, however, insists that Alonso is wanted. "The bottom line is that we are the best choice for him.
"If he would drive with us out of this crisis, he would be a hero," the Briton added.