Gratuitous USn bashing aside, I would say:

"I'm starting a new class in the fall"
or
"I'm starting a new class in the autumn"

I would probably reserve the articleless "in fall/autumn" for speaking generically of the season and use the article when speaking of a specific fall/autumn.

In fall I like to jump into piles of leaves.

In the fall, I'll be covering the Ithaca Bombers fall baseball season.