Centre Manu Tuilagi scored England's only try in the second half and Owen Farrell kicked four penalties and replacement Toby Flood slotted two as France slumped to their worst start in the tournament since 1958. But it was Robshaw's captaincy, which came under such scrutiny in the autumn, which pleased Lancaster most.
"He was outstanding," said Lancaster. "He and Tom Wood in the back row in the last 10, 15 minutes were everywhere. They were like rocks in the side."
He added: "It is what we build our game around. Chris was outstanding in his leadership and his ability to make correct decisions under pressure, as a player as well as a captain. It is testament to him."
Robshaw was named man of the match after a game in which the French went close to redeeming themselves for defeats against Italy and Wales.
Centre Wesley Fofana scored a first-half try while Morgan Parra kicked a penalty and a conversion and replacement Frederic Michalak also slotted a penalty.
And while Robshaw admitted England were caught cold at times in the first half, he was delighted with the way they finished.
Robshaw said: "It was a real test match. Credit to our defence in the second half because ultimately it created Manu Tuilagi's try and allowed us to keep the scoreboard ticking over.
"The character of the squad means we were never too far out of the game. We kept the belief that we can come back, even in the first half when we didn't play that well. It might have been different if we were on the road, but the crowd got us going. It is a great win.
"The Grand Slam doesn't cross people's minds, our feet are firmly on the ground. We are in a good place. Manu was great. You could really see his power and physicality. He wanted to prove a point and he did that. He was exceptional."