I want to install a couple motion sensor lights in a carport. The gable part of the roof's fascia crosses the same on the house. Since I already have a GFI protected 20A run in attic of house that only feeds 2 standard outlets can I just junction off this circuit and run conduit through wall, across eave, through the adjoining fascia boards, and across carport eave? I would add a switch once in carport.

That really depends on what the existing outlets are. If they are bathroom or small appliance circuits then no you cannot. Just about anything else and yes you can.