If the Republican ticket won California in 1996 they would have a good chance to win.Could Pete Wilson beat Clinton?
No. Clinton beat Dole by 8.5 percentage points nationwide.
https://en.wikipedia.org/wiki/United_States_presidential_election,_1996 I see no reason to think Wilson would have done *that* much better than Dole. Even if he carried California, that wouldn't even put him close in the Electoral College.
For that matter, I doubt very much Wilson would even carry California (which Dole lost by 13 points). Yes, he easily won the governorship in 1994, but (1) that was a Republican year, and (2) party matters much less in governorship races than for the presidency. States that are solidly Democratic in presidential elections often elect Republican governors. Does anyone really think that George Pataki would carry New York for president in 1996 or 2000, or that Bruce Rauner would carry Illinois for president in 2016? BTW, Wilson's job approval ratings in California, while not terrible, were hardly stellar in 1996:
http://www.field.com/fieldpoll/governors.html
Moreover, while there is such a thing as a home state advantage, studies have shown that the more populous the state, the less the advantage is. In the case of as large a state as California, the advantage would probably be small.
Generally speaking, when a party has had control of the White House for only four years, the president is likely to be re-elected if there is peace and prosperity (and no divisive challenge within the party) as was the case in 1996. It takes longer than that (usually eight years) before time-for-a-change sentiment really sets in.