This has come up before on Paizo's forums and the consensus is "no". Half Elves DO NOT get elven weapon familiarity. Compare the racial details for half-orcs which specify that half-orcs do get weapon familiarity. That isn't mentioned in the Half-elf details. If you argue that half-elves should get to use elven weapons, then that argument also says they should get +2 vs SR and +2 Spellcraft to ID magic items. Okay, you refer to the text of the spear itself - on that basis you are correct, but it contradicts the core rulebook on elven weapon use.
Paizo forums:
2009,
2010,
2013.