CRJ-700 flight crew reported low altitude alert on approach. Performed go-around and landed uneventfully.

Narrative

We were on a repo flight after the I.T. meltdown late at night. We took off and flew the flight uneventfully and go on the arrival at the end of the arrival we were cleared for the approach. The PF kept the airplane in FMS mode at ZZZZZ. I assumed it was a new technique and watched it since it was turning outside the final approach fix at the initial approach fix. We were high so we set the lower altitude. The FMS intercepted inside FAF and start to head towards the airport instead. I called for heading mode to correct this but act called go around low altitude alert. We went around uneventfully and came around for a successful landing.Root cause narrative: Loss of situational awareness due to fatigue and not speaking up sooner.Suggestion: Fatigue played an issue because we sat on the ground for 3 hours. I assumed we were still doing the right thing but I realized the normal procedure I should've called out for is heading mode to join the approach.