That material (Mypex) is designed to separate gravel, slabs etc from the underlying soil, so they don't just sink in. It is a woven fabric, so there are gaps between the threads which allow perennial weeds to come through easily. It's claims to be a weed suppressant are over-stated. And unless it is well covered, it shreds.
A non-woven fabric like plantex is better as a weed suppressant. We use it double thickness and covered by gravel for paths. Last time we wanted to get plantex, it was difficult to source. I think we had to order it from Europe. I'm not convinced it will work well as a vertical barrier which I think is what you are considering?
I don't like using herbicides, but it is probably your best option.
Alternatively, accept that you need to leave a gap of a couple of feet inside your fence and keep that weed free.
Disclaimer - we don't have a problem with ground elder, but several decades of fighting Horsetail, and that will come up through tarmac and concrete, so count your blessings!