Multiferroic phases combining magnetic and polar orders offer opportunities for optical control of spin and electric degrees of freedom. Here, using symmetry analysis and Floquet theory, we establish a Floquet spin-antiferroelectric phase coexisting with unconventional magnetism in periodically driven collinear antiferromagnets, qualifying it as an unconventional multiferroic. This driven phase supports compensated, spin-resolved in-plane electric polarizations perpendicular to the vertical rotation axis, which are strictly forbidden by crystalline symmetry in equilibrium. Using a tight-binding model, we elucidate how light polarization controls the emergence of polar order and spin responses. Moreover, first-principles-based Floquet calculations predict its realization in monolayer MnPS₃, identifying a realistic two-dimensional antiferromagnetic platform. These findings establish a nonequilibrium route to spin-antiferroelectricity beyond equilibrium symmetry constraints and connect Floquet engineering, unconventional magnetism, and multiferroicity through optical control of spin and polar degrees of freedom.