When my boyfriend and I visited France a few months ago, I noticed that a lot of savory dishes were drizzled with some black-brown colored sauce on top (see picture I took, which is a plain risotto). The sauce tasted fairly sweet and not salty.
My best amateur guess is that this is some sort of reduced sugary balsamic vinegar sauce, but it does not taste acidic at all. Maybe the vinegar evaporated while reducing?