France looked more likely to snatch a second-half winner but England remained solid to secure a point and now face Sweden in Kiev on Friday as well as host nation Ukraine on Tuesday in Donetsk.
Lescott said: "Overall it was a good performance and a very accomplished performance as well.
"Obviously France are unbeaten in a lot of games (21) so we knew it was going to be tough. Before the tournament, France were one of the favourites to win the competition, never mind our group.
"I think we've got to be positive and take confidence from the result."
Lescott added: "On paper it looks like we've come through the hardest game with a draw.
"But Sweden won't be easy and Ukraine are the home nation. We've still got two tough games.
"The key is to keep it in our hands and go into each game with everything to play for."