The show is canonically established to be part of the Prime Universe, but it can be argued that it belongs to both the Prime and Kelvin Timelines.
The Kelvin Timeline was introduced in the 2009 Star Trek reboot movie, directed by J.J. Abrams and starring Chris Pine as James T. Kirk.
The movie's twist revealed that it wasn't a traditional reboot, but rather an alternate timeline, with the original Star Trek TV shows and movies remaining part of the main canon.
This is confirmed by the return of Leonard Nimoy as Spock Prime, alongside Zachary Quinto's new version of the character.
Author's summary: Enterprise belongs to both timelines.