Carpe futurum is correct, but I'm not so sure you want to use that, since it's already the motto of an educational company.
Honestly, you might want to think about what you're actually saying in Latin and how students will take it. "Seize the future" means to pluck it, to take it into your hands. It's a very concrete verb, conjuring up images of plucking fruit. You can see the dictionary entry here:
https://www.perseus.tufts.edu/hopper/morph?l=carpo&la=la#lexicon
But regardless of its etymology, how is the word used? Its origin lies with the Roman poet Horace, who was trying to convince a young girl to sleep with him because life is short and time is finite. Great motivation for education, right?
Yes, yes, it was used in Dead Poets Society and it is used over and over again, overused, even, to the point of cliche. That's another pitfall, will anyone take it seriously? Will the kids you're trying to inspire get it from a Latin motto? Do any of them even take Latin? If they do, they'd appreciate a more authentic motto from their readings. If not, it's just a slight fancy-sounding variant on a well-worn (as in worn into the ground) cliche.
Maybe your company can spin it right. Maybe the pitch will inspire, and the words will take on new meaning. But if you really want to motivate, seize the language of the students and use that to encourage. Or find something distinct enough that their ears won't close after hearing it.
Even then you're taking a gamble. How many people still associate Ubuntu with its etymology meaning 'humanity'? But at least then you'll have something that makes people stop and ask, "Wait, what does that mean?"
Just my two cents, of course. Use it at will (not sure if there's a problem since the other company is already using it, but legal will be able to figure that out). Either way, good luck in your endeavors. Education needs all the help it can get.
(On a more minor quibble, it's 'reins', not 'reigns.' The former is what you hold onto to steer horses, the latter is what rulers have over their dominions.)