Carpet gets wet after a rainfall.

Doors don't normally leak as they have seals all around the edge, and the glass, unless yours are missing . Do you have a sunroof in it? Drains block or the pipes come unattached.

https://www.mazda6club.com/threads/drivers-side-carpet-gets-wet-when-it-rains.189807/

Or you have a blocked drain in front of the windscreen.

Or you have a hole in the floor.

Or the AC Drain is blocked.

How wet is the foot well? This is likely to be one of two things. Door seal rubber or the Heater matrix.
Try this bit of detective work. Does it only get wet when it rains heavily? Is it just the front that is wet? Feel the carpet in the foot well. How high up the foot well carpet does the wetness go? Does the wetness smell of anything? Do you have a sun roof fitted? Sun roofs have drain holes that can clog up so the rain pools up in the grooves and runners then over spills inside the vehicle.
If it only gets wet after rain it could be a worn out door seal rubber or the sun roof letting water in. Door seals usually cause shallow pools of water so the wetness won't rise very high up the carpet. The sun roof sometimes causes the seats to get wet as well.
If it is wet all the time, the wetness rises high up into the foot well and it has a 'sweet' smell, it could be the small radiator unit,(the Heater Matrix), behind the dashboard that supplies heat to the heater blowers leaking. Depending on where exactly it is fitted you'll sometimes get wetness in both front foot wells. The smell is the coolant from the engine.
Hope this helps.

I had similar on 02 Highlander. Source was leak from around window trim (rust) and roof racks connector entering and going down the windshield post behind the trim. Gently remove the interior plastic trim piece to the left of the windshield to see any water coming down there. Find source, disassemble whatever is required and use good sealant like supra expert.

Had similar on 02 Highlander. Source was leak from around window trim (rust) and roof racks connector entering and going down the windshield post behind the trim. Gently remove interior plastic trim piece to the left of the windshield to investigate any water coming down behind there. Find source, disassemble whatever is required and use something like SupraExpert to seal (not just cheap silicone).

The two most common causes are rain water leaking in or the ac drain being clogged up. I would vote for rain water if the entire carpet area is wet.
Could be coming in around the windshield, or one of the door gaskets.

If its cold during your rainy weather and you need heat to warm the interior of your car. You might want to have your cooling system pressure checked. The heater core might have developed some corrosion which will eventually lead to leaks. If you have radiator coolant in your cooling system, touch the wet carpet then rub your fingers together. There should be a film left on your fingers. Hope this helps.

does it have a sun roof and the drains are plugged up?

I think that I can help you. It sounds like your drain-tube is plugged up. Get in the passenger side, and pull the carpet back from under the glove box. Look for a black rubber pipe that goes from a black box, and pokes thru the firewall, on the passenger side. Remove the hose from the box, and have a container ready to catch water. If water comes out of the black box, your drain hose is plugged up. Clean out the clog, and you will be golden.

Have your ac evaporator deain cleaned out or checked. Without this working the ac water will collect there.