Had similarly problem with my recently acquired e86. The vapour barrier in the door had separated from the inner door skin along the bottom edge, so water was running down inside the door (as it should), but the gap in the barrier was letting it come out between the door card and the inner door skin, instead of keeping it within the door so that it exits via the drain holes at the bottom of the door, like it’s supposed to. This was dumping water right on top of the door seal on the sill, so some of it just goes inside the car, and into the carpet.
You can check if this is your issue by making sure the seal on the door sill and the door at the bottom of the door card are dry, then liberally dowsing the door and window with water. If you then find there’s water on the sill seal, or on the inside of the door at the bottom, below the the door card, this is likely your issue.
I took the door card off, found where the barrier had become detached, and pressed it back on. There is a strip of butyl sealent all the way round, but this probably loses its grip over time, and will eventually need replacing. I added some additional butyl sealer and ran Gorilla tape along the bottom edge, for good measure. You don’t need to remove any major door components if this is your issue, only the door card. There are several how-tos on the web about removing Z4 door cards, and I think there’s several threads in this forum about repairing this particular problem, if I recall.
Seems to be fine now, but I am thinking I might fit a new vapour barrier in the future, since the old one is a bit tatty, and I think the problem was caused by it being removed and replaced during some previous owner’s hi-fi ‘upgrade’. I’ll take the old barrier off, clean off all the old butyl and replace with new butyl tape and barrier.