Student housing doesn't generally include Ferienwohnungen / vacation rentals. That said, any "FeWo" you find right in Freiburg, while it may not be occupied by students, is likely to be more expensive and perhaps less available than comparable places in the vicinity of Freiburg. Look into the outskirts of Freiburg and into smaller towns nearby that are well connected by public transport (like the Stadtbahn / tram, or the regional railways) if you need easy access to Freiburg. These towns, 10-20 minutes out and connected by train:
Bad Krozingen
Waldkirch
Emmendingen
Here's a listing by an owner with two apartments in Bad Krozingen from the site I linked to previously - just an example of what you might find.
https://www.schwarzwald-tourismus.info/stg/ukv/house/Bad-Krozingen-Ferienwohnung-Ferienwohnung-Josef-und-Irmgard-Bihlmann-FIT00020070033673652#tp-anchor-description
Like this listing does, most listings indicate the distance of the rental from the rail station or other transport stop. There's also a link to the owner's private website, which in this case lists the same prices, but also indicates that discounts are negotiable for long-term stays (more than 6 nights.) Such discounts are very common when you book directly with the owners - sometimes with just 4-5 night stays. In your situation, I would ask about a long-term stay discount in every inquiry.
You'll be there a long time - so a major consideration is cancellation policy. Reservations in Germany are like contracts. If the establishment does not publish or communicate a specific cancellation policy, any booking makes you financially responsible by law for the full amount owed for the period booked. Book for two months, pay for two months. Most establishments these days DO have cancellation policies, thankfully, but whether the place you wish to book has one is something you cannot count on and that you MUST determine on your own - and not just prior to making a deposit or paying, but prior to booking.