Tape up the outside rim where the wall meets the floor, and then on the inside, use a can of expanding foam run under the gap.
The tape around the outside will keep the foam from expanding outwards. You can always trim up with a sharp knife.
Once the foam has set, and you have trimmed it tidy, you may then need to seal the foam - just to stop the slow deterioration by sunlight, but it will probably last for years even if you dont.