First and unless I recall incorrectly "Constitution Class" (for the Enterprise
) wasn't noticable until after
Gene Roddenberry no longer walked the Earth (i.e, "Relics" and ST VI).
While the passage in The Making of Star Trek
referring to "Enterprise Class starships" is not a literal quote from Gene Roddenberry, it's the outcome of the interviews and talks Stephen E. Whitfield conducted with the producers. Because the book lists Whitfield and Roddenberry as authors, everything that's in there must have met with the approval of the Great Bird of the Galaxy.
The Constitution Class (!) blueprints of Franz Joseph suggest Gene Roddenberry had approved but don't carry his signature. It's fair to assume Roddenberry merely tolerated this (hoping he'd still get a share of the profits which never happened).
In contrast the official TMP "new Enterprise [Starship II] Class" blueprints are not only authenticated by Andrew Probert but also approved by Gene Roddenberry - and this time with his signature.
On the other hand, the TMP novelization apparently written by Gene Roddenberry himself, makes an early reference to "Constitution Class", in particular Kirk wondering whether this particular Starship Class would still be a match for the new K'tinga Klingon Battlecruisers.
But this is not evidence that the Enterprise
belongs to the Constitution Class. Since we apparently do have a refitted Enterprise Starship II Class (NCC-1701) and a refitted Constitution Starship II Class (NCC-1701-A), this could merely indicate that the Constitution Class had stronger weaponry, shields or whatever.
Interestingly, the only thing we do know for certain about the Constitution Class is that it carried a Mark IX/01 primary long-range phaser, and that Scotty found this interesting enough to study it in detail in "The Trouble With Tribbles".