Fate x Naruto:
Different from where normally Shirou reincarnates or Naruto is summoned. This is a story where Sasuke died in a fight with Naruto and was reborn as Shirou in this new world.
However, he was only able to remember things vaguely and his power was only awakened via trauma.
The first is when he saw the Flame of Fuyuki where he awakens his Eternal Magenkyou, and remember thing vaguely.
Second when he awakens his Rinnegan and all his memory upon seeing Kiritsugu's death, and his promise to inherit Kiritsugu's dream.
You can write the character as you wish.
Either Sasuke becomes a demon lord who conquers the world, to forcefully save it, or becomes more like Shirou.