The French have three main police forces. The national (two of them) are armed, often more heavily than US cops.
Most of the municipal cops, which is probably what this lady is, are not armed. That may change.
Should note that being armed does not keep you from being shot. The cops killed in NYC were armed.
I recently lived on Sint Maarten for 6 months. The Gendarmes there were heavily armed and respected. Just not enough of them.