That is a gorgeous photo, and that’s a nice lightweight frame! That means that there are a few fixes you can try at home:

• You could pop in a few staples across that joint. If you’re using light-weight staples, like the ones for papers, they’ll likely stretch pretty quickly.
• A high-temp hot glue gun, some epoxy, or super glue would likely work.
• If you like hanging light-weight things, a picture hanging kit might be helpful. If you don’t want to even go that far, some fishing line and low-profile thumb tracks could work and save you money over the years. You’ll need to tie a loop in each end of the fishing line, so consider looking into a fishing loop tool if you have any dexterity issues.
• Command strips will hold that shit up, and take the paint from your walls when it comes down.
• If you’re concerned about damaging your walls, use a ridiculous amount of hot glue. I’m absolutely serious. It seems like a relatively permanent solution, especially when it’s time to take everything down, but rubbing alcohol cleans up hot glue really nicely.

Of course, getting new frames from thrift shops is always a decent solution. Or, if you feel like it’s worth the cost, consider printing it on canvas or metal. Lots of local print shops will do this in-house now.