How can we reconcile God's infallibility of the Prophet, may God's prayers and peace be upon him, from being killed, with what was narrated about his being affected by Jewish poison?

There is no contradiction between the verse, "And Allah will protect you from the people," and the Prophet's death, peace and blessings be upon him, due to poison. The infallibility mentioned in the verse is from temptation and misguidance, and from being killed before conveying the message. This is what happened, for the Prophet completed his message before his death. Allah willed nothing but to combine for His Prophet both prophethood and martyrdom, and to remind us of the enmity of the Jews.