Joleon Lescott gave England the lead with a header from captain Steven Gerrard's free-kick - but France were level before the interval with a fine 20-yard finish from Lescott's Manchester City team-mate Samir Nasri.
It was a game that dulled the early sparkle of this tournament, and was played out in searing temperatures inside the Donbass Arena by two teams who may well take satisfaction from a point from their first game.
James Milner wasted an early chance for England, while new manager Roy Hodgson was grateful to goalkeeper Joe Hart for a fine block from Alou Diarra's header.
Hodgson made the bold choice of Arsenal teenager Alex Oxlade-Chamberlain ahead of Stewart Downing. Opportunities for him to shine were rare but he can be pleased with his efforts in strength-sapping conditions.
Once again England were tactically disciplined and highly organised - an early trademark under Hodgson since he succeeded Fabio Capello.
And the manager knows this was a game safely negotiated as he waits for the return of striker Wayne Rooney after he completes his suspension against Sweden.
England's preparation for Euro 2012 were disrupted by injuries - and not even Hodgson's backroom staff were safe as veteran coach Ray Clemence injured himself in the warm-up and had to be carried off.
The failure to cut the supply line to Nasri did not cost England when he pulled an early shot wide.
England created the best opportunity of what was some early sparring, played out in an occasionally eerie silence in this giant arena. Such was the lack of noise from the stands that players could constantly be heard shouting instructions.