It really cracks me up that while the Star Trek reboot totally altered the Prime Universe from TOS and beyond, “Star Trek: Enterprise” is still necessarily canon.
“Star Trek Beyond” even makes overt references to ST:E. The Xindi Wars. The MACOs.
The U.S.S. Franklin is even an NX class vessel (although it’s weird that despite being able to only go Warp 4, it has a higher registry number (NX-326) than the Enterprise NX-01, which is capable of Warp 5.) The original crew of the U.S.S. Franklin wears the blue uniform of pre-Federation Starfleet.