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Résumé : Confirmed by the measurement of neutrino oscillations, neutrino mass is recognized as a genuine manifestation of physics beyond the Standard Model, while its originating mechanism remains a mystery. Moreover, the proper field-theory description of neutrinos, whether they are Majorana or Dirac type, must be linked to such a mechanism. The present work addresses the calculation, estimation, and analysis of one-loop contributions from virtual Majorana neutrinos, light and heavy as well, to the neutral gauge boson coupling $ZZZ$, which participates in $Z$-boson pair production from ${e}^{+}{e}^{\ensuremath{-}}$ collisions. This task is carried out in the framework defined by a seesaw variant in which light neutrinos remain massless at tree level, then becoming massive radiatively. The $ZZ{Z}^{*}$ coupling, with ${Z}^{*}$ an off-shell $Z$ boson, is defined by two form factors, namely, ${f}_{4}$, characterizing $CP$-odd effects, and ${f}_{5}$, which is $CP$-even. Constraints from the Large Hadron Collider on both of these quantities are currently $\mathcal{O}({10}^{\ensuremath{-}4})$. Our calculation yields $CP$-nonpreserving contributions to $ZZZ$, which are absent in the framework of the sole Standard Model. Our estimations show that the ${f}_{4}$ contribution might be as large as $\mathcal{O}({10}^{\ensuremath{-}7})$ for heavy-neutrino masses $\ensuremath{\sim}1\text{ }\text{ }\mathrm{TeV}$. $CP$-even contributions ${f}_{5}$ are also generated, which are, in general, larger than their $CP$-odd counterparts. We estimate them to be as large as $\mathcal{O}({10}^{\ensuremath{-}4})$ at a center-of-mass energy of 500 GeV, in ${e}^{+}{e}^{\ensuremath{-}}$ collisions.