What status did French Algeria hold prior to its independence. I read somewhere that it was considered as much a part of the nation as Corsica is today. Did French-Algerians have the same rights as their European brethren?

To answer the first bit: Algeria was considered integral French territory, making it just as much a part of France as Normandy or Champagne.

I'm guessing by "French-Algerian" you mean the pied-Noir ("black feet" i.e. the white people). And Pied-noir DID have all the rights of the metropolitan French.

There's a ton of potential detail, but instead of spilling it here I'll just suggest you pick up A Savage War of Peace by Alastair Horne. Fantastic reading.