Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
According to scholarly consensus, it is permissible for a Muslim to make a bequest to a Dhimmi (A non-Muslim living under the protection of a Muslim state) provided that it doesn`t exceed one third of the estate.
"It is permissible for a Muslim to make a bequest to a Dhimmi, a combatant and an apostate according to the more correct opinion." {Matin al-Menhaaj, V.6:48}.
Ibn Qhoddamah (May Allah have mercy on him) said: "It is permissible for a Muslim to make a bequest for a Dhimmi, a Dhimmi for a Muslim, and a Dhimmi for a Dhimmi. This (A Muslim making a bequest to a Dhimmi) was transmitted from Shoraih, al-Sho`abi, al-Thawri, al-Shafie, Is-hak, and others.
Mohammed Ibn al-Hanfiah, `Ata`, and Qhotadah said that the verse: "nevertheless do ye what is just to your closest friends…" refers to a bequest that a Muslim makes to a Jew and a Christian.
Sa`ied said: "Sofian reported from Ayoob from Ekrimah that Safiah Bint Hoyai sold her house to Mo`wiah for a hundred thousand. She asked her Jewish brother to convert to Islam to get a share from her estate but he refused, so she bequeathed a third to him. Since she is allowed to give him a gift, she is also allowed to write him a bequest just like a Muslim." {Al-Moghni, vol.6/pp.121}.
In conclusion, there is no sin on you (Asker) to make a bequest to your Christian wife because she isn`t allowed to inherit you as she follows a different faith, however, this is provided that the bequest is no more than one third of your estate. And Allah the Almighty Knows Best.