I don't know necesarily why Baccarat should come to mind (or Steuben for that matter), although of course it could well be French - but as a shape this was made in several countries, and could date anywhere from c. 1800, and possibly even into the C20. If it was early then you might expect the colour to be a little less bright than C20 glass and you should have the sort of wear that would be appropriate for a period piece. Although you don't give an indication of size, I'd suggest your glass is a rummer (possibly an incurved bowl), and as I say indications of age would depend on wear, colour and striations in the upper half of the bowl - also possibly on thickness/thin-ness of glass).
Can't see too clearly in your pix, but as you've indicated lead glass then the bowl decoration is quite possibly slice cut (although might be moulded) - if cut then you should find feint grinding marks on the bowl decoration - although you might need a pocket lens to see these.
Rummers (nothing to do with roemers) were a common European shape of drinking glass that typically have circular shaped feet, with square moulded feet like this found less commonly.
I understand that C19 Baccarat pieces frequently had a paper label, thereafter the backstamps were acid etched.........with both label and acid marks showing the 'stem + decanter + tumbler. However, can't imagine paper labels from the C19 surviving intact on a glass like this.
If this does have a ground/polished pontil and rings well then very unlikely to be pressed glass.
Sorry this is not conclusive of any specific date or manufacturer, but drinking glasses are prone to remaining without provenance, frequently - especially in the absence of marks.
However, a nice glass, and very typical of a rummer, so congratulations - and really up to you to decide whether it is period or a much later copy.
Ref. 'Miller's glass fact file a-z' - Ivo Hanstra - 2001.