The scrum-half scored the game's only try and was named man of the match as the Irish made it two wins from three.
"With the weather it was going to be difficult and we had a few chances which we did not convert," said Murray
"But we stuck in the fight and to win 19-9 is great and we are still in the hunt for this championship."
Murray added: "A win and nothing else would do this week and we have managed to do that.
"Johnny Sexton slotted back in really well and the 70-odd minutes he got will stand to him for the next two matches.
"The forward laid the foundation by getting into great positions.
"A win against France is always a good win.
"We have a week off to rest up and look at Wales, so we're still in the fight."
Conor Murray believes Ireland's 19-9 win over France has kept them right in contention to win the Six Nations Championship.