Wine should be fermented until either all the sugar turns to alcohol and there is no more food for the yeast, or the increasing alcohol content kills off or denatures the yeast. In either case fermentation stops at this point. So the final sweetness of the wine depends on the amount of sugar it contained in the first place combined with the alcohol tolerance of the strain of yeast.
My somewhat hazy memory of wine-making suggests that certain champagne yeasts tolerate a higher percentage of alcohol, hence the very crisp, bone-dry nature of good champagne as almost all of the initial sugar is used up in the initial fermentation. For a sweeter wine you would used yeast inactivated at a lower percentage of alcohol, leaving residual sugar in the wine (or sweeten post-fermentation after chemically killing off any remaining yeast).
Although for fizzy wine I think they add a little more sugar after fermentation stops and the stuff is bottled, to allow for it to restart limited fermentation within the bottle and make bubbles. But still, this extra sugar should be consumed by the yeast in a dry wine so the finished stuff will have very little.
So the drier the wine, the less sugar. Anyway I have tested myself and can happily report that dry red, white or fizzy plonk does not affect my BG so all is good in the ‘hood.