Insulating film isn't going to solve much, it's more just for looks 😅 Your real problem is the seal on the sashes, which over time as the wood shifts, leaves gaps all over the place.
The most practical solution is to start with self-adhesive weatherstripping (you can get it at any hardware store, it's cheap), but honestly with windows that old you'll probably find there are spots where the sash doesn't fit properly into the frame. If the wood is warped or the hinges have given way, it's not just a sealing issue. In that case it's worth getting someone to look at it and see if they can adjust the sashes or if it needs more serious repair before you put anything on.
As for replacing the windows, yeah, it gets pricey (around 200-400€ per window depending on size and quality), but they last 20-30 years and you save a lot on heating. If it's just one or two windows that are really drafty, maybe it's worth doing that and using weatherstripping on the others for now. But have a good look at the overall condition first - sometimes a good adjustment makes a real difference 👍