Why is my baguette type bread coming out almost flat?
If you haven't changed your recipe then the problem is in your method, and it sounds like you are over proofing. If your bread expands too much in the final rise it gets over-extended and tends to collapse when scored, exactly as you describe. It's easy to 'get greedy' and try to eke out that much more expansion, but it's actually a very common mistake.
Reduce your final rise after shaping and you'll get a better result.  Go for a doubling in size typically, maybe a bit more. It's hard to give a time on that, but typically 1.5 hours is the most I'd give it, I like to still have some visible rising going on when I put it in the oven because part of oven spring comes from the yeast.
If you do over-prove it's not a disaster, just don't score it, then put it into the oven gently.
As for how to proof the dough, you don't need to use the oven, in fact I'd recommend against that unless your house is really cold. 70°f is fine for proofing, it just takes a bit longer than a warm oven, and you often get more flavor and better structure if you don't rush it. One thing I would suggest is not to use a damp towel as the weight of it on a small baguette can hold it down a bit, and the evaporation of water from the towel cools the bread and slows down proofing. Instead proof your bread in a clear plastic bag (clear so you can see through it, no other reason). You blow air into the bag and then clip it, the air will keep the bag from contacting the dough and sticking. The bag will seal in the heat generated from the yeast activity as well as keeping in moisture, preventing it from forming a skin.