The best open source alternative to EVE Online is Oolite, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 25 alternatives to EVE Online and three of them is open source so hopefully you can find a suitable replacement. Other interesting open source alternatives to EVE Online are Vega Strike (Free, Open Source) and Alite (Free, Open Source).
Oolite is a space sim game, inspired by Elite. Among Oolite's several similarities to its inspirational source, the gaming experience is enhanced by the context set in Elite's original manual, and the accompanying novella, The Dark Wheel.