As far as I know, the Constitution in SFB is a CA (with whatever refit etc), so the Enterprise in TOS would be a CA. I'm pretty sure in the X-module it lists the Enterprise-A under the CX section, and as far as I can figure, the Ent-A was another refitted Constitution (like the refit Enterprise in ST-1) renamed to Enterprise-A after the loss of the original ship. So, assuming thats the case, then the TMP Enterprise could be considered a CX under SFB.
Also depends on the service dates of the Enterpise and the Constitution refit dates. I beleive the films are set about 2280 to about 2290 (according to my ST-RPG, the Genesis event, ST2, is 2285 and the Khitomer Accords, ST6, is 2293), so if you can figure out the corrisponding year in service dates for whatever refits etc, maybe that'll help.
Open to correction
Thu11s