After successfully managing to gain custody of Harry, Remus and Sirius have raised Harry well. He knows that he's loved, and well-treated, and he's friends with Ron and Neville. However, a visit to Gringotts on Harry's tenth birthday to get him confirmed as the heir to the Potter and Black Houses proves that Dumbledore has done something awful to Harry, and they realise they must remain cautious of him.
This leads us to Harry's very well-known first year at Hogwarts, but this time with Draco, Neville, and Hermione by his side.
Just a note: Most of the relationships will start to happen in the third book. It's my plan to work through all the canon books. This first one starts out echoing canon very closely, but will become quite AU after the first few books.
Also, I'm cross-posting this on AO3 under my username, MaraRiall, just in case you find it there.