France, who will host the global showpiece in September, ran in seven tries in a 53-10 demolition, punishing a woeful England for all their mistakes to claim their first win at Twickenham since 2007 and their first there in the Six Nations since 2005.
After a defeat against championship leaders Ireland, France bounced back with a win against Scotland. But Saturday's performance was on a different level.
"We wanted to play a big game today and that's what we did. It's our biggest performance in a while," said full back Thomas Ramos (27), whose second-minute try set the tone for the afternoon.
Ramos added 18 points with his boot while Thibaud Flament (25) and Damian Penaud (26) notched up two tries each and Charles Ollivon (29) also touched down.
Captain Antoine Dupont (26) said he had "trouble realising what we did when I look at the scoreboard".
But Galthie said he was fully aware of what had just happened. "Yes I realise. I've been coming here since I was 20," he said with tears in his eyes.
"We played the way we wanted to play... We didn't know exactly how but we had that drive. And doing it here, in this context...
"It didn't happen by chance. We've been working together with these players. It shows we're on the right path...," added Galthie.
He spared a thought for England, who have been trying to rebuild after coach Eddie Jones (63) was replaced by Steve Borthwick (43).
"It's tough for them when you know how important rugby is in England," Galthie, a former France captain, said.
France next face Wales at the Stade de France and could still win the Six Nations if Ireland slip up in one of their two final games.
"We'll be tired tomorrow but it's always easier to recover after such a big win," said Dupont.
