What is 1.27mm ribbon cable impedance for the "ground-signal-ground-signal-..." configuration?
Not quite.  With a ribbon cable, and similarly for a twisted pair, the wires couple to each other, rather than coupling to a ground/return plane.  And so the impedance of a signal wire is approximately 120 ohms.  Thinner insulation brings the conductors closer together and results in a slightly lower impedance.

Note that this is different than a single ended, or diff signal trace over a ground plane.  In that configuration, the signal trace couples much tightly to the ground plane, and it is this coupling that determines the single ended and diff impedances, with the diff impedance being ~2X that of a single ended trace.

EDIT1 - Answer to OP's question

Yes, you're right about a ground wire on either side of the signal trace.  That will reduce the impedance, but won't halve it.  This is sorta like a stripline/microstrip discussion.  A 5 mil wide trace with 5 mil heights will give a Z of 41 ohms for a stripline configuration, and 69 ohms for a microstrip.

You should be able to find some on-line impedance calculators to help you.