France led by eight points going into the final 10 minutes as Uruguay pushed them all the way.
With a better set-piece – both scrums and line-outs – they might have pulled off one of the great World Cup shocks.
In the end their inaccuracy let France off the hook, but it was still a performance to savour for Vilaseca.
"I'm so proud of my team. I couldn't ask for a better team to lead. That's the truth," he said.
"Today, with 10 minutes left of the game, we were fighting against France, one of the best teams in the world, playing at their home ground. This is only the beginning for us.
"We fought for the whole game, it was key for us to keep pushing France and keep battling."
Uruguay scored the opening try of the game through wing Nicolas Freitas and added another in the second half via fullback Baltazar Amaya.
They had numerous other entries into the France 22, but could not make them count.
France top Pool A with eight points from their two games while Uruguay have a second fixture against Italy in Nice next Wednesday.
On this showing they will be confident of pulling off a win.
New Zealand and Namibia are the other two teams in the group.
