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I try to do something simple, use official data of Belgium zones that I found here: https://eservices.minfin.fgov.be/myminfin-web/pages/cadastral-plans.
So I downloaded the files of one city and opened it in QGIS. That works but the coordinate system seems to be totally wrong. I would like to switch to an international standard.
In fact, I need to use the Googlemap API to get coordinates from full addresses and use that to get the position. Is there a way to correct that?
I downloaded a random shapefile from your link and plotted it against a basemap:
The coordinate system is fine. Perhaps you can provide an example of a shapefile that you think is incorrect.
As for your second questions about getting coordinates: if you want lat/lon, the most common coordinate reference system (CRS) to use is EPSG:4326. You can transform your shapefile(s) into 4326 using the "Reproject layer" tool in the "Vector general" QGIS toolbox. You say you want to use the coordinates to "get the position," but the coordinates are the position so I'm not sure what you mean exactly.
PROJCS["Belge_Lambert_1972",GEOGCS["GCS_Belge_1972",DATUM["D_Belge_1972",SPHEROID["International_1924",6378388,297]],PRIMEM["Greenwich",0],UNIT["Degree",0.0174532925199432955]],PROJECTION["Lambert_Conformal_Conic"],PARAMETER["False_Easting",150000.01256],PARAMETER["False_Northing",5400088.4378],PARAMETER["Central_Meridian",4.367486666666666],PARAMETER["Standard_Parallel_1",49.8333339],PARAMETER["Standard_Parallel_2",51.16666733333333],PARAMETER["Latitude_Of_Origin",90],UNIT["Meter",1]]which might not be want you want.incorrect. It isn't a custom CRS and is described in the EPSG database ~ epsg-registry.org/export.htm?wkt=urn:ogc:def:crs:EPSG::31370