I have a few points of logic you should consider, especially about Griffins, but first:
[The Europeans have] Crossbows.
That doesn't stop the Druids, with healing magic. How powerful or fast is the healing magic? Is it a weapon itself, in war? I have shot both a regular bow and a crossbow, it is not instantly easy to hit the bullseye with it. So while a bolt to the head of a druid might kill it; that is a small target, and can be protected by a shield or helmet. Suppose along with healing, druids can also magically turn off pain in war: They might as well, any injuries are going to be healed anyway, and any damage caused to their bodies by ignoring pain will be magically disappeared as well.
Unlike the Europeans, make the Druids extremely hard to kill; it isn't enough to put a bolt in their heart and move on; put ten bolts in them and they are still coming at you with an axe like its a minor inconvenience. A European soldier could get so used to Griffins as to not think of them as magic, but the Druids in war could seem unstoppable.
Griffins are sentient and volunteer in the army, they are quite able at strategy and act as guerrilla units in war time.
Then why aren't they in charge? What stops them from militarily just taking over from the Europeans and subjugating them? I infer they must be better at "strategy" than the Europeans, which makes them more intelligent than their masters, and better fighters to boot, since you intend them to be the reason the Euros dominate.
Given all that, why isn't this a Griffin nation? Or alternatively, why don't the Griffin break away and form their own nation? Do the Europeans prohibit the Griffin from holding political positions within their culture? Are the Griffin considered second-class citizens? Is it okay for them to be guerrilla warriors or soldiers, but never okay to be Mayor or President? Can a Griffin be our modern equivalent of a billionaire, rich and powerful with many human servants and a huge estate? Or, despite their sentience, and capacity for self-sacrifice (volunteering to protect others), and superior reasoning ability (required for superior strategic foresight), are they still treated like horses, forever relegated to the animal kingdom because of their phenotype?
Whatever makes the Griffin loyal to the Europeans, inequality and second-class status can be a powerful driver for them toward independence or a better lot.
Perhaps that political reality is coming to a head: Let us posit that the Griffin, intelligent but warriors at heart, admire the Druids in war as fellow warriors. They note the Druids fight their own wars head on without fear; including their Kings and Priests on the front lines. This is something they don't see in any other culture, especially amongst their own soft and fat Euro masters that stay far from the action.
A Potential Plot Path
The Griffins are second-class citizens in the Euro culture.
Put is in a time of initial skirmishes between the Euros and Druids, with Euros invading the more peaceful Druid territory. The Griffin population is unsettled; and developing an admiration for the Druid warriors; a stark departure from their experience with Euros and other cultures. In one of these skirmishes, a young Griffin doing his duty in the military, but also unsettled as to Griffin status in the Euro community, is badly injured by Druids; with broken wings and a spear through him, unconscious and left for dead on the battle field.
The Druid King, walking the battle field in the aftermath in case any of his soldiers can be healed, finds this Griffin; and using his healing magic; brings him to consciousness. The broken Griffin awakes in horrible pain; the King lays hands on him and the pain vanishes to barely a throb. The King converses with the Griffin, half interrogation, and half questioning the motives of the Griffin.
But this Griffin is not that sure himself about his own motives; he is loyal to a community that does not treat him as an equal. He speaks freely, certain he will die of his injuries anyway. In his mind a Griffin with broken wings is a dead Griffin, period.
In the end, the King chooses to not kill the Griffin. Druids are nature lovers and love animals. The King knows the Griffin may return to war, but so might a horse, and he understands that the horse does not choose battle, it is enslaved and cannot do anything else. So the Druid do not slaughter injured horses left behind by the enemy. They heal them and set them free.
He asks the Griffin if his kind has made the choice to invade Druidic land. Are they capable of their own decisions? The Griffin claims they are. The Druidic King ponders this, but then says, "You have given me no reason to believe that is true," and with a touch of his finger on the shattered wing of the Griffin, the Griffin falls unconscious. He wakes up hours later, the moon high in the midnight sky, fully healed. The spear through his lungs is gone; His wings intact and fully functioning, even the scratches and cuts of battle are gone. He leaps into the sky and climbs, then circles the battle field, there is no Druid or campfire in sight. He heads away, toward the European encampment.
Thus begins the neutralization of the Griffins. This one returns, his story is told and kept amongst the Griffins. They believe him, the Griffin seldom lie to their own kind, and are never cowardly.
The Druid King by touching the Griffin has learned the magic they need, and in war hereafter, a touch of more than a second or two from a Druid leaves a Griffin unconscious. After battles, any Griffin not killed in the battle, awakens healed.
The Griffin allegiance to the Euros has softened, and they are not inclined to fight Druids. They are sentient, they know full well the Druids could behead them on the battle field, but the Druids choose to heal them instead.
So while not all Griffins agree on everything, and some disdain the Druids for being weak and sentimental soldiers, the majority of Griffins have been neutralized by Druidic Mercy. And every time it happens, they question why they are following the orders of the European King at all. Are they really just smarter horses, blindly subservient?
There is a growing sentiment among Griffins that "The Druid fight is not our fight, there are other lands to conquer." A separatist movement is brewing, and the Europeans know it; so they have that distraction of social inequality to keep them politically occupied.
The Druids are smaller, geographically isolated, with no particular weapons or desire to conquer the world.
The Europeans have a standoff with the Druids, and Druids alone, because both Crossbows and Griffins are of limited use against Druids, and an all out assault on Druids might lead to a Griffin revolution. They can still wage war and plunder other human tribes; so they do that instead, it is their path of least resistance.