The question appears to be about visas rather than COVID-19 travel restrictions. Your wife needs a separate visa to enter France.
Before the UK left the EU, she would have been able to travel to France using a "residence card of a family member of a union citizen." But the EEA family permit (the document that was analogous to the EU Settlement Scheme family permit) did not confer an exemption from the visa requirement. Furthermore, the residence permit that she will eventually receive under the EUSS will not entitle her to enter the Schengen area without a visa, because the UK is no longer a member of the EU.
As others have noted, you should also pay close attention to COVID-19 travel restrictions, both those imposed by France and those imposed by the UK.