I have a 2003 tbird.When it rains the carpet gets wet. This happened with the old top.I just did a test with the garden hose.I applied water along the rear window.The carpeted floor was wet again.

SOURCE: Interior Carpet Getting Wet

It sounds like a plugged drain line from the air conditioner. Most cars now run in the a/c mode whenever u turn on the climate control (even when heat is on). The passenger side front is where it would be wet, and the carpet and carpet pad act like a sponge and will soak up the water. Let me know how u make out.

SOURCE: 96 chevy tahoe, passenger side and rear cargo carpet is wet

sounds like the air conditioning drain for condensation is plugged

SOURCE: Front passenger side carpet getting wet

The AC evaporator units have a drain hose that runs through the floor because condensed moisture is a fact of life with AC units. Yours is plugged. You will have to get under the vehicle and look for the hose where it comes out, then take like coat hanger wire and clean it out, It is somewhere in the vicinity of where the passenger foot well meets the fire wall. If you have to raise the vehicle to get under it, make certain you have it safely supported. If you don't have the stuff, drive the passenger side wheels up on a good curb and use some cardboard to slide under.

SOURCE: Wet floor on driver side only; Prevelant after heavy rain

I had a similar problem, water running off windshield down drain hole only came in when parked with front lower than rear. A hole used to route a wire to engine compartment from driver side through rear of fender allowed water to come in. Remove rear fender liner fastners from left front fender pull liner away without fully removing it and look for hole leading into cabin. Plug it with deaft sealer.
My 2001 had a wire for an alarm system routed through hole, but dealer who sold me car as used felt he could not leave an non factory alrm system in place DUH!
Ken

SOURCE: water leading into car between the firewall and

I was getting a drip into the passenger side footwell. It got worse as time went on. I started looking at the coolant hoses from the engine into the firewall which provide heated coolant to the heater core. One of the hoses was cracked at the firewall causing the coolant to leak down into passenger footwell. Rather than continue to deal with smell and flood into cab I simply looped the hose from the engine back to the other input and bypassed the heater core entirely. Now that it's 28F I miss my heat and defrost. So think twice before doing it my way.