There's a really nice boulangerie in the area, Mamiche, but it's gone a bit viral so you might need to wait in line. If you've got no patience, on the same street there's KB Caféshop which is a specialty coffee roasters so more coffee focused but they also have pastries and light breakfast options.
There's also Buvette Paris but that's more of a brunch type place. If you're there with the DC I suppose crepes at Cafe Breizh might be an option? There's also two good ice cream places, Une Glace à Paris and Glaces Glazed. Bulot Bulot is a nice seafood bar in case you need another lunch/dinner option.
In terms of sights, well, it's all a bit cliche, Sacre Coeur and Moulin Rouge/Rue Lepic being the main sights, you'll barely hear any French around you but it is pretty and the view from the Sacre Coeur is beautiful. For the rest, it is more of a residential area than people realise (and lots of steep hills so sensible footwear and supportive socks recommended). The cemetery is interesting though, if you enjoy that kind of thing.
For shops, there's a few surplus/outlet shops. There's a Maison Kitsune one close to KB Caféshop, brands like Maje, Sandro, etc. also available. The only one I bother making the trek for is the A.P.C. surplus, prices are good and it is a good brand to pick up for basics, for men especially in that location. In that street and the street parallel to that (can't remember if it's below or above) there are cute little independent shops, a lot ran by Japanese expats for some reason who have a really nice curation of things but these shops seem to come and go a lot.
There's a lot of secondhand vintage in the area but it's mostly crap for tourists at inflated prices. I do like RoseMarket Vintage which has designer vintage, quite unique pieces, a bit more free spirited than other designer vintage shops in Paris. Kind of that luxe 70s Parisienne vibe. On the pricier side, especially compared to the other vintage places in the area (technically I'm stretching the boundary of Pigalle with this one though).
Let me know if you need any specific address of the above as I know Google maps can get itself confused quite a bit in Paris.
WRT to Italy, I've always sort of viewed it as it's such a family focused society that there's sort almost an obligation to present as a unit and reflect each other in that way. So you'll see less of that contrast of a man just wearing any old thing with a female partner dressed to the nines.