Assassin’s Creed Unity is currently plagued with frame rate issues on the PS4, Xbox One and PC. It is also a victim of plenty of technical and graphical glitches. Ubisoft has acknowledged the issues faced by players in Assassin’s Creed Unity and has started a live blog to update with fixes to most of these issues.
According to this reddit thread, if you are having issues with the frame rate particularly on the PS4, you can trying putting your PS4 offline to fix it. Additonally, you can try rebuilding the databse. Other users have confirmed that this fixed their stuttering and frame rate issues on PC as well so this solution can work on other platforms too.
Assassin’s Creed Unity is the first game in the series to introduce online co-op. It also relies on online extenseively, which perhaps explain this quick home-made fix for the game. If you are one of the users experiencing stuttering and slowdowns on the PS4, you can try this trick to see if this fix your issues or not.