Probably not a false result but it may have been a chemical pregnancy (is the spotting still going?) Chemical pregnancy is just a term for the early stages of pregnancy. If AF starts then it is a M/C but very early. If you weren't trying you probably wouldn't even have noticed you were pregnant.
But just because you are spotting doesn't mean you will definitely M/C. Good luck and let us know what the GP says and what happens.
All the best
Debbie