That was in complete contrast to the first half where the Swiss defence had been highly organised and had frustrated the French attack – and it was them who went into half-time in front thanks to a composed finished from the talented Géraldine Reuteler who had been the Swiss' main threat.
The French coach Gilles Eyquem introduced Mateo and Morroni at the start of the second half, and it took just 35 seconds for the two to combine for the equaliser through Mateo's header. Minutes later, Mateo set up Marie-Antoinette Katoto as France took the lead before Mateo got her third goal soon after.
More ruthlessness in the second half, in particular from Morroni, could have seen France win by six or seven goals, but as it is, they went on to win 3-1 to reach their eighth final as they try to win the tournament for the first time since 2013.
Switzerland, meanwhile, are still looking to reach their first ever final, having lost their previous three matches at this stage.
France start strongly
Switzerland actually had the game's first chance from a free-kick on the right wing. Lesley Ramseier's delivery picked out the unmarked Cinzia Zehnder, but she seemed to get under the ball and head over the bar.
France nearly went up the other end and scored with Delphine Cascarino finding space behind the right wing, beating Julia Stierli's challenge before seeing her shot magnificently tipped onto the post by Natascha Honegger.
But soon, France started to struggle to open up Switzerland's disciplined defensive display that was set up narrow, not leaving gaps for France to exploit with their pace and requiring them to go wide.
However, Les Bleues did manage to breach the Swiss defence, and they should have taken the lead in the 16th minute. A long ball from the right-back Héloïse Mansuy sent Katoto down the right-wing and she showed great skill to cut the ball back to Grace Geyoro, who somehow got her feet mixed up and shot wide from a glorious position.
And then moments later, after the first ball into the box had the cleared, the ball fell to Laura Condon on the edge of the box, but her shot was well tipped over by the Swiss keeper.
Switzerland shock France
Having survived these chances, the Swiss seemed to grow in confidence and started to gain more possession in the French half. A mistake from the French gifted possession straight to Reuteler who broke into the box, but possibly took too long to get her shot off, allowing Mansuy to make a superb goal-saving block.
Then, when Reuteler was brought down outside the box by Estelle Cascarino, Switzerland nearly took the lead through Naomi Mégroz's effort that just curled wide.
And with the last kick of the first half, Switzerland did take the lead when Marilena Widmer's pass sent Reuteler behind the French defence, and she waited for the French keeper Mylene Chavas to commit, before dinking the ball over her with a remarkably composed finish.
France redefine impact subs
The Swiss coach Nora Häuptle could not have expected what would happen just 35 seconds into the second half, as the French rewrote the definition of impact sub. Both Mateo and Morroni had been surprisingly left out of the starting XI, and both were brought on at half-time, and the two combined for the equaliser. From the byline, Morroni put in the perfect cross to the far post where Mateo's header gave Honegger no chance.
The speed of the equaliser seems to shock Switzerland as their organisation disappeared and France started to open them up. Geyero played in Morroni with a delightful through ball and she really should have done better as her shot went wide of the right post.
Minutes later though, France did take the lead. Morroni played Mateo into the box and she rounded the keeper but took far too long which allowed the Switzerland defence to recover. But she didn't panic, and she held the ball up before setting up Katoto who found the bottom left corner.
Then it was 3-1, and it came from a Swiss free-kick. The delivery from Ramseier was eventually cleared by France and they launched a swift counter. Katoto played Mateo through and her first time shot from the edge of the area nestled in the bottom left corner.
Switzerland slowly regained some composure, and nearly pulled a goal back from a corner, but Ramseier's header just went wide of the near post.
Morroni misses glorious chances
But France still looked like scoring every time they came forward and only good fortune kept Switzerland from falling further behind. Delphine Cascarino crossed to Morroni whose shot was saved by Honegger's leg, rebounded onto the post, back onto the keeper, back onto the post and out for a corner.
Morroni had another glorious chance as Louise Fleury's lay-off set up her, but her shot hit the crossbar.
Switzerland had a glorious chance in the 87th minute, but the ending summed their half up. Sina Spieser's cross went through Estelle Cascarino's legs and to Camille Surdez who shinned it well wide, perhaps expecting the ball to be cut out by the French centre-back.
With the last kick of the game, Condon's long range effort nearly added a spectacular fourth, but when the whistle blew, it was the French players in joyous celebrations – with the Swiss team trying to work out what had happened.