Laurent Blanc's Bleus extended an unbeaten run to 21 games ahead of the Group D match against England with Evra's dangerous cross leading to the fourth goal by Jeremy Menez.
The United defender was preferred to Manchester City's Gael Clichy at left-back and looks set to start in Donetsk next Monday.
"We're going to the Euros with confidence, while having a lot of humility, which is most important," he told sports.fr. "We are moving from game to game and that's fine. We will try and make a good performance but it's not about saying it in interviews, we also need to show it in the game.
"It was three warm-up matches. We're happy to finish this preparation with three wins but we still have a few days to prepare for this match with England, which is really important to us."