Derivational situation not clear yet. Should Huehnergard2011 be right in connecting ‘infidelity’ to ‘village’ then the following items may be derived from
kafr :
► kafara, i (kufr, kufrān, kufūr), vb. I, to be irreligious, be an infidel, not to believe: denom. from kāfir or kufr (?).
► kaffara, vb. II, to make an infidel, seduce to unbelief: caus., denom. from kāfir or kufr. – For another value see ↗kafara.
► ʔakfara, vb. IV, to make an infidel; to call an infidel, accuse of infidelity: caus., denom. from kāfir or kufr.
► BP#3044C kufr, kufrān, n., unbelief, infidelity.
► kaffār, n., infidel, unbeliever: ints.
► takfīr, n., seduction to infidelity; charge of unbelief: vn. II. – For another value see ↗kafara.
► BP#3646C kāfir, pl. ‑ūn, kuffār, kafaraẗ, kifār, adj./n., irreligious, unbelieving; unbeliever, infidel, atheist; ungrateful: PA I (but see "Discussion").