Under my rubber mat??

Find and fix the leak first, than dry out the floor boards, remove lose rust, and coat with rust encapsulating coating such as POR-15 on rusted surfaces only. This will stop further corrosion of floor metal, moisture proof the surface, and provide a good clean attachment surface for installing carpet.

Possible leak points to look for: wiper pivot at base of windshield; windshield gasket; air box, crawl, and vents from perforation or buildup of plant debris; holes or poorly sealed seams in floor pans; at seat bolt down points, and the hole here headlight dimmer sticks through rubber mat that can let melting snow penetrate padding, and small holes in rubber mat where one show heal rests a base of accelerator.

Often a perforated mat and a window left open during rain will be enough to soak padding, and moisture trapped under rubber will not evaporate for a very long time producing a moldy old car stink that will never go away until padding is replaced & both sides of mat are washed with soap & water.

Me, a convertible guy, accustomed to wet floors for 35 years.