La solidarité, il s’agit d’aider des gens moins fortunés que nous.

Fortuné(singulier) : Someone who have a lot of money.

Answering the side question, an even better way to say this would be :

La solidarité consiste à aider les gens moins fortunés que soi.

“soi” refers here to the person(s) showing solidarity.

I would suggest one of:

− La solidarité consiste à aider des personnes moins privilégiées que nous.

− La solidarité consiste à aider des personnes dans le besoin.

− La solidarité consiste à aider des personnes ayant moins de chance que nous.

Fortuné means in modern French almost exclusively "possessing a large amount of money" so doesn’t properly match the English "fortunate" (lucky/happy/healthy/…)

Curiously, Infortuné has kept its original meaning so does match the English "Unfortunate".