Can't see detail of the hairspring, unfortunately but are you sure it's broken and not just deformed?
If it's deformed, then it may be possible to recover the shape. If it's broken right next to the stud, then it could be re-pinned to the stud as a few mm on the total length would not be an issue - there's a bit of work to do on the balance after that but not insurmountable and it can even be left at the shorter length without a balance adjustment but, the regulator won't be in the middle at a good rate.
If it's broken somewhere else:
Hairsprings are available for just about any watch but, they come as a "blank" (for want of a better word). They are just a coiled spring and are sold based on stiffness in a fairly complex way so, to get one you need to do a fair number of calculations to determine the spring to buy - they don't just tell you the thickness and height. After you get it, you need to form the inner coil and pin it to the collet, then form the outer coil (in your case a Breguet making life more difficult again by a factor of 10!) and pin that to the stud after getting the length right by checking how it vibrates. That's the very short and simplified version and might explain why they come in packs of 5 or 10... That will cost a lot and you will struggle to get someone to do it as it's not something that watchmakers do every day. I don't and don't know anyone that does.
Another option is a donor watch with a good balance and hairspring. I think the Bulova may have the same base calibre and it'll be cheaper to pick up a donor movement for a Bulova than a UN. Here is a
9AT taken from the link. It is a similar layout and I think all the wheels are in the same place but the bridges are clearly different. If all the wheels are the same, then it may very well be an FHF 1246 base calibre for both the UN and the Bulova. Worth checking that on a Bulova and UN forum before buying a donor.
Hope this helps (a little anyway!), Chris
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