Question: "How do I fix a leaking door membrane?"
Answer: The answer to this question really comes down to how competent you are as a car mechanic. And let's be honest, if you were a car mechanic, you wouldn't be asking the question. It is actually just a sheet of plastic which probably costs the manufacturer pennies to produce. However, since it has been imported from whatever country it was manufactured in, passed through distributors, dealers and parts companies, had the price of admin added onto it plus tax, it's really rather expensive for what it is. So many mechanics make their own... as I said, it's just a sheet of plastic. So if you were going to 'Do it yourself' you would need to source a roll of plastic and a tube of the appropriate sealer, which combined would probably arm you with enough material to do twenty door membranes but cost you as much as a replacement part imported from France.
Then there's the business of removing the door card to access the leaky membrane. These door cards are usually made of recycled plastics and cardboard, because we all want to save the planet and recycle. However, this can mean that the materials are not the very best quality and can be a little delicate, which is not normally a problem because they aren't often removed so don't have to be particularly soldier-proof. It does help to have a little experience and the right tools in order to get them off without damaging them. The clips that hold them on may well break, they frequently do. This is fairly normal, and they are easy to replace if you happen to have spares, as most mechanics do.
...and so it goes on. Yes, you can do it yourself, but you are probably better just taking it to your local mechanic and asking them to do it. It can be difficult to answer questions like this without sounding patronizing, but it is what it is.