In the first trailer we saw the Millenium Falcon soaring over the desert evading laser blasts from two TIE Fighters. In the second trailer we saw more of that chase as the Falcon flies up the exhaust of a crashed Imperial ship. But we also saw more. We see Han Solo and Chewbacca on board with blasters drawn.
We also saw everyone's new favorite droid, BB-8, peeking around a bulkhead, likely looking at our heroes.
And in the behind-the-scenes featurette, we see Rey (played by Daisy Ridley), the young female lead who is described as a scavenger, in the cockpit of the Falcon. One scene shows her flying solo (forgive the pun) at one point, and at the end has her in the co-pilot's chair next to Han Solo.
You can bet that part of her scavenging included finding the Falcon on Jakku and repairing it. It's finder's keeper's in a scavenger's world, especially if you fix what you find. Even though she and Solo will both be on the same team, I anticipate some humorous-and maybe tense-back-and-forth between those two regarding whose ship the Falcon really is. In the long run, I think it's going to be hers.