The safest way to fix a curtain rail

If by "stack," you mean that the curtain hooks get out of order, which makes opening the curtains back up impossible, then you could put a small screw or nail in the top/window side of each hook (perhaps two in each hook if it is really bad.) Or you could just get bigger hooks. That would make it would be impossible for them to overlap.

If the problem is that too much friction is created by pulling on the curtain material, then I would suggest finding a curtain pulley system (or attaching a rod to the middle-most hook on each side of the curtain.) Such systems would create an entirely horizontal force on the curtain's hooks, as opposed to the diagonal downward force created by simply pulling on the curtain material, which will create friction between the hooks and the rail. Or, if the rail and hooks are metal, you could simply try oiling them to reduce friction.

If the problem is something other than the hooks overlapping and becoming inseparable, please explain the problem... maybe even a picture would be in order!

Windows need framing around them, to support the hole-in-the-wall the window represents. This means that support framing (IF you have wooden framing) will be immediately to the left, right and above the window, within the first several inches.

Small test nailings can be done in the area in question, just deep enough to prove wood-or-not. Drillings with small bits can accomplish the same thing, as well as making a pilot hole for a screw.

Failing-finding-wood, anchors of various configurations will support the screw(s) in drywall (also known as plasterboard, wallboard, gypsum board, or gyprock), such as: