Attack v defence: Both managers agreed that Austria came into the match looking for a draw, leaving little mystery regarding which side was happier after the 1-1 stalemate. PHOTO: AFP
Captain Lara Dickenmann and Ramona Bachmann scored as Switzerland recovered from a goal down to beat Iceland 2-1 in the earlier game.
France and Austria top Group C with four points, one ahead of Switzerland, while Iceland will bow out after the group phase.
France dominated almost the entire game in Utrecht, but it was Austria's Lisa Makas who scored first in the 27th minute, drilling home from just inside the area the French failed to clear a throw-in.
Henry then slammed in a header from a corner delivered by Elise Bussaglia on 51 minutes.
France's Marie-Laure Delie had two good chances early into the game but was denied by Austrian goalkeeper Manuela Zinsberger.
Austria threatened twice before scoring, with French keeper Sarah Bouhaddi stopping Laura Feiersinger's shot and Makas missing the target with a flicked free-kick.
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In the second half, Zinsberger brilliantly tipped Henry's curling shot onto the crossbar, while French substitute Kadidiatou Diani was denied by the keeper and then missed the goal altogether in stoppage time.
"I'm frustrated. We deserved to win. I thought Austria didn't really play, preferring instead to sit back and wait," said French coach Olivier Echouafni. "Austria waited and we gave them the chance to score."
Austrian coach Dominik Thalhammer did not object, saying his team had settled for a ‘defensive performance’. "France are a world-class team but we managed to put them under pressure for 15 minutes of the first half and at the end of the second too,” he said.
Earlier in Doetinchem, Iceland took the lead on 33 minutes as Fanndis Fridriksdottir beat Gaelle Thalmann in the Swiss goal with a low left-footed strike.
Ten minutes later, Dickenmann fired home a cutback from Bachmann.
Bachmann then scored the winner on 52 minutes after an excellent exchange in midfield, with Noelle Maritz providing the final cross for the Chelsea striker to head home.
"It was a very exciting game for the fans, but it was certainly a test of everybody's nerves," said Swiss coach Martina Voss-Tecklenburg.
"Technically we could do much better, passing and receiving and running without the ball," said Iceland coach Freyr Alexandersson. "But the atmosphere was good and the support for the Icelandic team was world-class. We are very happy for their support, we really wanted to give them a victory tonight, but that was not the case."
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