Expectations have to be at all time low, so that may actually help and the players might be more relaxed. If they beat the French in the first game watch for the band wagon to take off and the pressure will be back on.
France has a very good team, young, fast, skillful, with practically two good players in every position. They will have a strong bench and there will be quality players coming in to tip the balance if needed if any of the group games are still up for grabs in the last 20 minutes.
Ukraine has the advantage of playing at home. They also have a good midfield, with everyone talking about Andriy Yarmolenko as one of the "new" players to watch at this tournament. They also have Konoplyanka and Gusev in their midfield and England's midfield could have problems getting the ball back. Throw in Shevchenko who is supposed to have regained some of his form and Ukraine won't be a push over.
Sweden always gives England a tough game and I don't expect any different this time. The Swedes do play attacking football so Ibrahimovic will get his goals, but like Ukraine they aren't very good defensively.
The French are a very good dark horse to win the competition and I expect them to win this group. It's a toss up who finishes second. Hodgson, I suspect will set England up to play with two defensive midfielders and try to score on the counter. Both Sweden and Ukraine play attacking football and are supposed to be weaker at the back than England, so that maybe the edge that gets England second in the group.
However, with Spain or Italy waiting in the quarter finals, just getting out of the group stage might be as good as England can hope for.