The shifter for the front derailleur is "soft" in my vintage bike
At first glance I see the problem you are having .

Those are NOT friction shifters . They are positron shifters .

Research Shimano Positron Shifters for a more definitive explanation  

This was Shimano's earlier attempt at an indexed gear system.  Also known as "Positive Pre-Select" or PPS.

The main differences are that the indexing is in the deraileur rather than in the shifter on the handlebar.  As a result, the bowden cable is a full housing and has a thicker solid inner rather than a woven stranded cable.

Upshot - you can't just fit any old cables to the rear mech.  However its possible the front deraileur is just a standard non-indexed friction shifter.