There was no one "resistance" movement.
The woman with Rick in the market, hard and cold and adroitly dosing herself with hypocrisy, we have seen, is in the next scene like a little girl with the grown-ups.
She and her Jewish husband Marcel Dalio had really taken the terrible journey described in the opening narration of the film, fleeing France ahead of the occupation, obtaining letters of transit note in their case, very likely from Portuguese consul , whose heroic actions and earned him a Righteous Among The Nations commendation from the state of Israel and being stranded in Mexico with bogus Chilean passports before finally getting to the U.
The film initially depicts him as a sinister character the fact Sydney Greenstreet did play a villain opposite Bogart in another film doesn't hurt , but by the end he turns out to be an ally, providing Ilsa and Victor with important guidance regarding the letters of transit.