According to the FAQ, certain effects can increase the enhancement bonus past their initial value, like the Bane weapon property:
Weapon Bonuses: Can weapon special abilities (such as bane) or class abilities (such as a paladin's divine bond) allow you to exceed the +5 enhancement bonus limit and the +10 bonus-equivalent limitation?
For the enhancement bonus limitation, it depends on the specific effect or ability that's altering the weapon.
Bane: This allows the weapon to exceed the +5 limit, but only against the designated creature type. For example, a +5 dragon-bane longsword is normally a +5 weapon, but has a +7 enhancement bonus against dragons and deals +2d6 points of damage against dragons.
Paladin: The divine bond ability says "These [enhancement] bonuses can be added to the weapon, stacking with existing weapon bonuses to a maximum of +5." That means if a paladin has a +5 longsword, she can't use her divine bond to increate the enhancement bonus to +6 or higher (but she could use her bonuses to add abilities such as flaming to the weapon).
The +10 bonus-equivalent limitation is a hard cap for all weapons; you can't exceed that even with class abilities or other unusual abilities.
If we read this with that explanation in mind, what is normal for Furious is the enhancement bonus while not raging. And thus, this additional bonus is stacking on top of the non-raging bonus.
When the wielder is raging or under the effect of a rage spell, the weapon’s enhancement bonus is +2 better than normal.
According to the restrictions on the enhancement bonus for magic weapons found on the 4th printing of the core rulebook (post errata), we have:
A single weapon cannot have a modified bonus (enhancement bonus plus special ability bonus equivalents, including those from character abilities and spells) higher than +10.
This is a special bonus and works similarly to how Bane works, except that the condition isn't the target's creature type, but the attacker's raging status (on/off). As such, this should fall into the same situation as the Bane property described on the FAQ and on this post from 2010 (also pre-errata) by James Jacobs (Paizo's Creative Director).
That said, a +1 longsword that is affected by Greater Magic Weapon should have an enhancement bonus of +3, which should have a modified enhancement bonus of +5 while the user is raging.