Is it permissible for a Muslim to recite the Adhan in the ear of a newborn non-Muslim child, and is that act considered an innovation (bid‘ah)?

The questioner's action is incorrect, as no authentic hadith has been established regarding giving the adhan in the ear of a newborn after birth. All narrations to that effect are weak or fabricated. Even if it were established, it would pertain to the children of Muslims, not the children of disbelievers. Furthermore, the adhan for the children of disbelievers does not benefit them, and not hearing the adhan does not harm the children of Muslims. Imam Malik considered giving the adhan in the ear of a newborn to be disliked (makruh). The questioner's intention and zeal are sincere, but his action is not prescribed (غير مشروع); therefore, he is advised to cease performing it, especially with the children of disbelievers.