Trippin' Through Time

She may be eating an ortolan, that's why she covers her head:

The traditional way French gourmands eat ortolans is to cover their heads and face with a large napkin or towel while consuming the bird. The purpose of the towel is debated. Some claim it is to retain the maximum aroma with the flavour as they consume the entire bird at once, while according to The Daily Telegraph, "Tradition dictates that [the towel] is to shield – from God's eyes – the shame of such a decadent and disgraceful act", and others have suggested the towel simply hides the consumers spitting out bones. This use of the towel was begun by a priest, a friend of Jean Anthelme Brillat-Savarin

https://en.wikipedia.org/wiki/Ortolan_bunting#Culinary_use

But wiki of the painting says:

The one on the left of the man wears a headscarf in the typical garb of married Roman women at the time.

https://en.wikipedia.org/wiki/In_a_Roman_Osteria

I think it doesn't look like that, it seems like it's just placed there, without any fixture.