The fastening plate has a screw molded into the backside which screws into the carpet.
I'm sure you can find them cheaper but here's where you can buy replacements as it sounds like the screw has broken off yours.:
https://www.ecstuning.com/b-genuine-porsche-parts/floor-mat-fastening-plate-priced-each/98655198500/
BMWs of recent era also use them and they are approximately the same size so they can be interchanged and/or found on fleabay:
https://www.ebay.com/itm/BRAND-NEW-BMW-GENUINE-OEM-FLOOR-MAT-HOLDER-VELCRO-LOCK-18F10-FREE-SHIPPING/132697065839?epid=5020510932&hash=item1ee55c896f%3Ag%3ANzAAAOSwjzJbJ5rn&_sacat=0&_nkw=bmw+velcro+mat+tab&_from=R40&rt=nc&_trksid=m570.l1313
Good luck