The French were able to celebrate a Six Nations Grand Slam, while England were left to reflect on their third defeat in five matches in the tournament.
Lawes was once again the Red Rose captain, producing a typically industrious 80-minute performance.
But it wasn't enough to steer England to victory.
"We're pretty disappointed to be honest," said Lawes, who will now return to Saints ahead of next Saturday's Gallagher Premiership game at London Irish.
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"We certainly had them in fitness - we felt like they were getting tired and we just failed to capitalise.
"It's on us and we've got a lot to learn from obviously.
"But I'm proud of the boys' effort still.
"It's hard to say straight after the game but we'll go back and iron out any kinks.
"It is what it is and we'd have obviously have loved to go out and get the win.
"I really thought we were going to do it at a few stages in the game but we didn't capitalise well enough.
"We really believed we could spoil the party - and I know we were capable of it because we've got the team for it.
"We just need to be more clinical, execute better and we can't let them off the hook that many times.
"They got so many turnovers at the breakdown and we didn't deliver there."
George Furbank played 77 minutes for England against France, having started the game at full-back.