The script would have improved if Rey had stolen The Millenium Falcon from Han Solo during her escape from Jakku and Han Solo had tracked her down to retrieve his ship. . . .
Interesting, but why exactly would he be on Jakku?
What if Han himself were looking for the droid?
He might be informed by Leia of its position on Jakku and, since he already is in a near system, he decides to rescue it. If you add one day between the beginning of the movie and Finn meeting Rey, Han should have enough time to arrive by hyperspace and starting looking for the droid. Than you can have, for example, Han finally finding the droid, and Finn and Rey following him on the Falcon when the fighters arrive.