In this study we show from first principles calculations the possibility to induce multiferroic and magnetoelectric functional properties in the Pnma NaMnF3 fluoroperovskite by means of epitaxial strain engineering. Surprisingly, we found a very strong non-linear polarization-strain coupling that drives an atypical amplification of the ferroelectric polarization for either compression or expansion of the cell. This property is associated with a non-collinear antiferromagnetic ordering, which induces a weak ferromagnetism and thus, making the strained NaMnF3 fluoroperovskite multiferroic. We also calculate the magnetoelectric response and we found it to be composed by linear and non-linear components with amplitudes similar to the ones of Cr2O3. These properties show that it is possible to move the fluoride family toward functional applications with unique responses.