The Ospreys man has retained his place in the team for the trip to Italy later this month, and Biggar has targeted becoming a regular for his country.
"I never doubted myself. When you doubt yourself, it becomes a very uphill battle," said Biggar.
"I've always believed I've some ability to step up and it's just nice we managed to put it together at the weekend. I thoroughly enjoyed it from minute one to 80.
"I'm under no illusions, my performance wasn't perfect. There were some errors in it but in games like that there are going to be some. I think we made a couple less than France did and managed to edge it."
Wales travel to Italy on February 23.