The stranded fighter can land safely, no combat is triggered and the attacker's plane returns home
When attacking and destroying an aircraft carrier, defender's fighters may remain in play after combat (if the attacker cancels the attack before all fighters are destroyed or no more units remain that can attack each other). These fighters are then considered stranded and, at the beginning of the Non-Combat Move Phase before the active player's moves, get the chance to move 1 space to a safe landing place. A safe landing place is either a friendly carrier or a friendly territory.
The rules define three states for territories: friendly, hostile and neutral. A territory is considered friendly when it is under your or your allies' control and control changes by capturing territories. This implies that a friendly territory with hostile planes "attacking" it is still considered friendly.
Furthermore, air units are allowed to attack hostile territories in the Combat Move Phase but it cannot be captured without land units there. The rules do not state anything forbidding that air units attack an empty hostile territory, even though it cannot be captured and no actual combat will happen. In the Non-Combat Move the air units have to return to friendly territory.
All combats triggered in the Combat Move Phase and all movements in the Non-Combat Move Phase are considered to happen simultaneously. Order of execution for individual events within these phases is irrelevant.
The result of this situation: before the attacker does any of his non-combat moves, the defender moves his stranded fighter. As the adjacent territory which is currently occupied by a hostile air unit, is still considered friendly, it is allowed to move there and be safe. No combat is triggered, as per the rules the defender's move into and the attacking plane's non-combat move out of the territory happen simultaneously and they never actually meet. The attacker's plane returns home, the defender's fighter remains in play.
This interpretation has been confirmed by Kevin Chapman, one of the game's developers, at the BoardGameGeek Forums.