In general, things only do what they say the do, and the specific outweighs the general.
When attacking a target beyond normal range, you have disadvantage on the attack roll. You can’t attack a target beyond the weapon’s long range.
RAW: The original attack must be made against a creature within the weapon’s range, or else there will be disadvantage on the attack roll.
If the attack misses, the Arcane Archer can use their Curving Shot ability to
reroll the attack roll against a different target within 60 feet of the original target.
RAW: So long as the new target is within 60ft of the original target, the Curving Shot ability works as described. There would not be disadvantage on this attack since Curved Shot does not say there would be disadvantage imposed. However, since you are rerolling the attack roll, if the original attack had disadvantage so too would the reroll.
RAI (and what I would do): This may allow an Arcane Archer to extend the range of their missed attack by 60ft, but I think this also fits thematically with the Arcane Archer as a fighter imbued imbuing magic into their archery.