It is not permissible to give zakaah on one’s wealth or crops, or Zakaat al-Fitr, to kaafirs, even if they are poor, or wayfarers, or debtors, and if one who gives zakaah to them, that is not counted as zakaah. 

It is permissible to give regular charity – not obligatory charity (i.e., zakaah) to poor kaafirs, and to exhange gifts and with them and treat them well to soften their hearts towards Islam, so long as they have not carried out any hostile actions against the Muslims, which would disallow that. Allaah says (interpretation of the meaning): 

“Allaah does not forbid you to deal justly and kindly with those who fought not against you on account of religion nor drove you out of your homes. Verily, Allaah loves those who deal with equity”

[al-Mumtahanah 60:8] 

And Allaah is the Source of strength. May Allaah bless our Prophet Muhammad and his family and companions, and grant them peace. 

From Fataawa al-Lajnah al-Daa’imah, vol. 10, p. 30 

There is one category of zakaah that may be given to the kuffaar, which is “to attract the hearts of those who have been inclined (towards Islam)” (cf. al-Tawbah 9:60). It is permissible to give zakaah funds to those kaafirs who hold positions of authority and influence among their people, if there is the hope that by giving them something they may become Muslims, then those who are under them may become Muslim too. And Allaah is the Source of strength.