(1) If a non-Muslim respects the translation the Holy Quran and you are satisfied that he shall not disrespect it and that he shall only touch it after making ghusl and he does ghusl or wudhu each time he reads it then it is allowable to give the Holy Quran to such a non-Muslim with the hope of guidance. And if you are not satisfied about all these conditions then never give it to him.
(2) Due to unavailability of the above mentioned conditions, the folder was found lying on the road. It shall be considered disrespect if done intentionally. The folder of the Holy Quran must not be given to a non-Muslim if there is fear of disrespect. And if there is no fear of disrespect rather you are satisfied then it is allowable to give.
ويمنع النصراني من مسه وجوزه محمد إذا اغتسل ولا بأس بتعليمه القرآن والفقه عسى يهتدى (الدر المختار مع الشامى 1/321 زكريا)
Allah knows Best!
Darul Uloom Deoband