. Due to heavy rains in our area the carpet of my car is all wet

You will have to remove the seats.
As well as at least part of the console and the door sills. The carpet will come right out.

If you go to a car wash where you can rent a vacuum, they are wet/dry vacs and will dry it out and a day with the windows down, (on a sunny day), and it will be fine.
Maybe some Lysol if it stinks at all.