The clean sweep was secured after a minute's silence was held before kick-off in memory of Davies, the 1976 Grand Slam captain, who died on Thursday at the age of 65 after a long illness.
"He was a legend of the game, our thoughts go this family, this one's for him," said Lydiate after the game.
Alex Cuthbert scored the only try of the match in the first half, while Leigh Halfpenny added the conversion and three penalties to seal the win.
Lydiate added: "We're just over the moon to be honest. The boys put their body on the line, you have to do that to win a Grand Slam.
"We're quite a young team so this is the first chance for a lot of us to win anything, we're over the moon."
Hooker Matthew Rees, who won his 50th cap against the French, added: "I've worked so hard to get back. My second Grand Slam, 50th cap, I think I'll be doing some partying tonight.
"It was frustrating for me with the calf injury, for me personally it was just about getting myself back fit and being part of a successful team.
"We're still a young side, there's plenty still to achieve and we're looking forward to the World Cup in 2015."