When used with upright bars & reverse levers, a "townie".
With drop bars, racks, and 700c or 650b, it's a "randonneur" bike. not the same as a "touring" bike though, which will generally have a more relaxed geometry and be designed to carry more gear.
If it's got a huge flat rack up front (like a Paul, Cetma, or VO), it's a "porteur" which is essentially a dressed up cargo / delivery bike.

i'm not entirely sure what sets a randonneur bike apart from a constructeur.

a catch-all term would be "Rivendell"