Ubisoft just released the 1.02 patch for Assassin's Creed Unity, and below you can check out the full changelog for both PS4 and PC.

PS4:

  • Fixed an issue where under some circumstances, Arno can fall through ground when free running on various props or when dropping down on to an NPC.
  • Fixed an issue where it is possible for Arno to get stuck in a hay cart next to the Pantheon in the Bièvre district.
  • Fixed an issue that may cause a game crash when joining the co-op session of another player who has a specific single player and side missions progression.

Note that even with this patch, players may still experience

  • Most framerate issues that have been reported since the release of the game
  • Performance issues

PC:

  • Fixed an issue where under some circumstances, Arno can fall through ground when free running on various props or when dropping down on to an NPC.
  • Fixed an issue where it is possible for Arno to get stuck in a hay cart next to the Pantheon in the Bièvre district.
  • Fixed an issue that may cause a game crash when joining the co-op session of another player who has a specific single player and side missions progression.
  • Improved performance in cinematic on low HW configurations
  • Fixed various flickering issues on nVidia SLI and AMD CrossFire configurations
  • Fixed various Graphic issues
  • Fixed light artifacts in PCSS shadows
  • Fixed problem with refresh rate on a first game launch.
  • Fixed various Input issues
  • Other keyboard/mouse fixes in several menu pages.
  • Fixed issues with “Invite to game” option when it was becoming unavailable after host migration, when it was active for all recent players instead of only for friends
  • Fixed issues with Helix Credits

Note that even with this patch, players may still experience

  • Most framerate issues that have been reported since the release of the game
  • Performance issues

Ubisoft also released an update on the work being done on fixing the performance issues affecting pretty much all platforms:

As previously reported on the Assassin’s Creed Live Updates Blog, our team is furiously working to resolve bugs and performance issues for Assassin’s Creed Unity on all platforms. On PC, some media outlets have misinterpreted a forum post indicating that we were working on resolving issues that were AMD-specific. We apologize for any confusion and want to be clear that we are working with all of our hardware partners to address known issues that exist across various PC configurations. We care deeply about a smooth and enjoyable Assassin’s Creed experience and we will continue to update customers as these issues are fixed via the AC Live Updates Blog.

While reports on social media seem to indicate that the patch improved frame rates (but that's definitely difficult to gauge with the naked eye), Ubisoft appears to think that more work is due there. The publisher also released a known issues list, where you can check out what's still to be done and what has been already solved on all platforms. You can find it here.