Switzerland got off the mark with a narrow 2-1 victory that eliminated Iceland but face a battle to get into the quarter-finals.
Iceland and Switzerland both needed a positive result in Doetinchem, having lost their opening Group C games at Euro 2017.
In a tough encounter with few goal-scoring chances, it was, Iceland who went ahead on 33 minutes, Fanndís Fridriksdóttir breaking into the box and finishing well.
The first ever Euro finals goal for Switzerland arrived 2 minutes before the break, as Lara Dickenmann levelled from close-range.
Ramona Bachmann put the Swiss 2-1 up early in the second half, stooping to head in a Noelle Maritz cross.
Play was held up for several minutes around the hour mark, with Swiss keeper Gaëlle Thalmann flattened after a clash of heads with Gunnhildur Jónsdóttir.
Bachmann hit the bar in added time but Iceland still threatened after that with a run of three corners, coming closest to scoring when a back-flick by Sara Bjork Gunnarsdóttir was cleared from the six-yard box.
Austria and France have identical records at the top of Group C, ahead of the final games against Iceland and Switzerland respectively.
After a competitive opening 15 minutes, France had the first real chance but Marie-Laure Delie’s stab at a Gaetane Thiney pull-back brought a sharp stop from the boot of Austrian keeper Manuela Zinsberger.
Sarah Bouhaddi then gifted Austria a chance but rescued the situation by getting down to push away Laura Feiersinger’s shot.
However, France were soon behind, as in the 27th minute a Verena Aschauer long throw found its way to Lisa Makas, who fired into the bottom corner from 16 yards out.
Les Bleues began the second period well and equalised 6 minutes in, Amandine Henry heading home from a corner after Zinsberger failed reach the ball.
A clever run then took Henry past three defenders but her shot was turned onto the bar by Zinsberger.
Nadine Prohaska came off the bench for Austria to hit a 25-yard half-volley, forcing Bouhaddi into a flying save.
With time running out, Eugenie le Sommer hooked a difficult ball over the top, Delie headed wide from Camile Abily’s cross and Kadidiatou Diani drove narrowly wide as France had to settle for the single point.