Can't tell what year your GR is from that tiny pic...but if it's around '74 it would have a TA 3-arm crank, this one looks like it could be a 6-arm cyclotouriste.More pics, please.
Rigida rims tend to be a little softer than others from the same era, but if they're laced to decent hubs I'd just use them and try to avoid curb-hopping and pot-holes.
Chances are that your Bianchi seatpost will not fit this metric-tubed Frenchie...the GR usually takes a 26.6 or 26.4. Stock post was not NR Campy even tho it came stock with Campy RD and FD...and Weinmann CP brakes.