Fans are most likely fine. Check if there is a good air flow through the radiator when fans are on, just to rule out very clogged air passages in radiator.
Also check the direction of air flow: it should come from radiator toward the engine. I had a very weird behavior of A/C for a year and nobody could figure out the reason: after some time idling with A/C on the A/C started to blow warm air and constantly do "on" and "off" within 10 sec period. I found out that previous owner replaced the fans (or whatever he or his mechanic did) and connected fans with opposite polarity, so they blew FROM the engine toward the rad.