FME does have the GeometryValidator transformer that can repair invalid geometries:

https://docs.safe.com/fme/2022.1/html/FME_Desktop_Documentation/FME_Transformers/Transformers/geometryvalidator.htm

To incorporate your models in FME, you’ll need to first export them to python. You can then use the PythonCaller to call those scripts. You will need to instruct FME to use QGISs python instance, theres some information on doing that here:
 

Thanks @hkingsbury for you answer. Unfortunately, the GeometryValidator transformer does not repair all of the invalid geometries. So I had to create a QGIS model that uses the following tools:
1. Fix geometry
2. Delete duplicate geom.
3. Remove null geometries
4. Fix geometry
Otherwise there is an error when loading the output data into a postgis database. I didn’t manage to get the python command of the QGIS model running in FME yet.

Can you be a bit more specific about the geometries that are not repaired? Maybe there’s another way...

I have this GeometryValidator. And the following issues, which data land at “Failed”.

Why does that feature fail the OGC checks (which the GeometryValidator can’t repair indeed)?

Where can I find that out specifically? 

You can scroll a bit further down in the Feature Information to check the coordinates. It’s hard to say because “fails OGC check” can have different causes of course.

My bet is that it may have to do with the fact that (part) of that object is a Bezier curve. I don’t know off the top of my head if there’s a transformer to fix that, maybe the ArcStroker. 

I tried the ‘ArcStroker’, that didn’t work. So I put the ‘Geometry Refiner’ after and it worked successfully.
Now I hope it also works with lines.

Thanks a lot for your help! :D