I'll be taking the car to a local carwash shortly to check the seals, etc. That isn't my problem.
I know you didn't ask for this advice, but:
I had this problem for a long time on my VW GTI and couldn't find the leak, until someone mentioned to me that modern cars are built with what's called a "Wet Door" design. Meaning the inside of the doors are designed to be very wet all the time. If you take off the interior door trim, there is a flimsy piece of plastic and a generally substandard glue/stickystuff seal holding it in place. If the floor of your car is wet, odds are it's coming in from there. You have to figure out how to get the interior door trim off and re-seal that bit of plastic so the rain doesn't get in any more.
My problem is that I want some tips for drying out the carpet.
Keep in mind that the carpet isn't the only thing under your feet. On my GTI, there was also a half-inch-thick layer of fibrous padding under the carpet. If that get soaked, you're fscked and your only solution is to remove the trim bits around the edge of the carpet, lift up the carpet, and dig out the sopping wet (and by now likely moldy) padding. Which, by the way, isn't designed to be removable, it's glued to the floor pan. Have phun....