I just posted a long message explaining what went wrong and everything was deleted. I hope this will work this time.
Here is the archive. As you can see, I had to do several ugly things.
First, I had to redraw the profile with a fit point spline because Fusion wouldn't flange if the angle between to line is less than 1° (WTF).
Then, I had to flange it long enough so that it could intersect the planes "ProfilMilieuGauche/Droite" ("Left/RightMiddleProfile"). I could then do a split and remove the part on the sides. I find it very ugly and it would have been much more convenient if there was the same "To Object" extent option as for the normal extrude.
One more ugly thing I had to do was to add a point very close to the point at the tip at the back of the profile, so that I could make the spline line not closed, because otherwise, it would do a very ugly bend at that point, and it wouldn't have fit precisely enough the profile:
One more downside of the fit point spline is that the flange doesn't fit the profile well enough anymore, causing the cut I had to make not precise enough:

As you can see, there are two different faces, distant by about 1 micron. The tool body touch the sheet where it shouldn't, it should be perfectly tangent to it. That cause a big performance issue as it crashed everytime where I performed a flat pattern. It didn't crash before I made the cut.
Strangely, it worked with the other body:

As you can see, the face remained connected (not simply connected because of the hole) and the hole circled in red was at the right place.