Manchester City team-mates Joleon Lescott and Samir Nasri traded first-half goals, and though his team were outplayed for long periods, England boss Roy Hodgson will be happy to take a point against the group favourites.
Sporting a 4-4-1-1 formation with nine men behind the ball for much of the game, England were limited in attack, but defended well despite surrendering their lead nine minutes after Lescott's 30th-minute header.
The technically-superior French struggled to turn their possession into clear goalscoring opportunities, and must find more cutting edge if they are to be considered serious contenders for the tournament.
Amazingly, France have still not won a European Championship match in which neither Michel Platini nor Zinedine Zidane was playing.
Hodgson opted for Alex Oxlade-Chamberlain on the left side of midfield - yet the decision to select a player with just six Premier League starts to his name was both popular and logical.
Oxlade-Chamberlain provides a bold directness Stewart Downing singularly lacks, and showed his intent to run at France with some early forays.
However, the game started slowly at a less-than-full Donbass Arena populated largely by Russian fans.
Amid a limp atmosphere, both teams showed excessive caution until Ashley Young carved out a golden chance for James Milner on the quarter-hour mark.
Young played a perfectly-weighted through ball for the sprinting Milner, who took the ball past Hugo Lloris but could not find the empty net from the left side of the box. A poor miss.
France bucked up after that, dominating possession and keeping the ball far better than their opponents, with Nasri and Yohan Cabaye particularly influential.
However, it was England who took the lead when Lescott met a peach of a free-kick from Steven Gerrard with a powerful header that game Lloris no chance - the goalkeeper possibly at fault for not claiming the ball at the edge of the six-yard box.
Back came Laurent Blanc's men, and five minutes later Alou Diarra stung the hands of Joe Hart with a powerful header of his own, before nodding side seconds later.
England were not off the hook for long, and on 39 minutes Nasri levelled, drilling a low shot into the near side of Hart's goal from just outside the box.
The midfielder celebrated his goal by aiming a 'shh' gesture at the English bench - a possible reaction to comments from Gary Neville describing Nasri as "a cancer" at Arsenal, shortly before his move to City.
England backed off, with the tepid noise around the ground mirroring the poor fare on the pitch.
The biggest danger to England was arguably Milner, who gave the ball away several times in the second period, but France came no closer than when Karim Benzema struck a long shot at Hart, and Cabaye had a powerful strike deflected wide.
Scott Parker came off late on, clearly exhausted and lacking full match fitness after recovering from an Achilles injury.
Benzema tested Hart with another effort from distance in the last minute, but there was no way through.
Hodgson's England might be the most limited squad ever to reach a major tournament, but their fight and organisation may yet take them into the knockout stages.