Dimitri Yachvili accepted France had been fortunate during their 9-8 World Cup semi-final win over Wales.
Wales, already hampered by the early loss of influential prop Adam Jones to injury, were up against it after skipper Sam Waburton was sent off in the 18th minute for a lifting tackle on Vincent Clerc.
Morgan Parra's three penalties proved just enough for Les Bleus to advance to next Sunday's final, where they will take on either hosts New Zealand or Australia.
"We feel first very proud," said Yachvili. "We started this competition very badly but we are proud because of the team spirit in the French team.
"We didn't play our best rugby tonight but we won so we are very happy.
"We know Wales maybe deserved to win because they had the injury, they had a red card - but we won and we are very happy.
"In 1987 France were in the final and those players for us are legends, but now it's us."
France captain Thierry Dusautoir felt solid defence had been the key to victory.
"We're really happy to be in the final," he said. "It was a really tough game but we are going to play a Rugby World Cup final so we are really happy.
"We won thanks to our defence. We didn't play such good rugby, the way we can, but we played with our hearts."