'70s vintage Raleigh Supercourse, 27" frame (crank center to top of seattube).
March 2011: The rear brake cable hanger on a built-in bridge has always puzzled me; never found a Motobecane model with that. Finally looked at some pics of Raleigh Supercourses and sure enough, some years have that bridge. The lugs and fork crown also match some years of Supercourse. The only pertinent brand markings on the bike, since the frame is painted over and the head badge is gone, are the Raleigh bar-end shifters. I always guessed they were replacements but now I'm thinking they were originally on down-tube clamp-ons, then converted to bar-end. Still plenty of puzzling details but for now I'm calling it a Raleigh SC.
'80s-ish UniVega "Alpina Trail", 21":
Either of 'em can hitch up to this Instep trailer, with its kids sling seats removed and a birch plywood floor laced in with zip-ties for a dog or cargo (you can see the edge of the plywood, just above the frame rail, photo right):