Here is the pertinent article from the National Electrical Code:
334.15
(C) In Unfinished Basements and Crawl Spaces. Where cable is run at angles with joists in unfinished basements and crawl spaces, it shall be permissible to secure cables not smaller than two 6 AWG or three 8 AWG conductors directly to the lower edges of the joists. Smaller cables shall be run either through bored holes in joists or on running boards. [emphasis added]
Now the key here is what constitutes a "running board". Most inspectors would probably require at least a piece of 1-by material like 1 x 4 or wider in an open area, to be called a running board but this phrase is open to the inspector's interpretation. Stapling to the side of 2-by material on top of the foundation wall, as in your case, would be even better since it is protected from physical damage by the concrete wall.
If it is not going to be inspected, and there is room to staple another cable there, then you are free to do what you want anyway. It will be just as good as the wire that has been there since 1960 and apparently that has not been a problem.
Finally, it should be stapled within 12" of panels or boxes and no less than every 4.5 feet thereafter to meet Code requirements. If you use hammered metal staples do NOT mash the wire. Snug is what you're after.
Good luck and stay safe!