She saw him before 1968. [ past tense]

She saw him before 1968. = OK She HAD SEEN him before 1968. = OK She HAS SEEN him before 1968. = NOT CORRECT Why? Remember that present perfect describes events that happened at an indefinite time before NOW. You are talking about an indefinite time before a point in the past, 1968, so you can't use present perfect. Use PAST perfect to describe events that happened up to a point in the past. Simple past is also OK.

I'd go with saw.

Either way the sentence does not seem quite right to me. Is there more to it than just this one sence? If not then it would have to be "saw". Even then it does not seem quite correct. "She had seen him once before 1968." or "She saw him once before 1968." would make more sence to me.