There's several ways to fix this, depending on a few things.
The best thing to do is avoid drywall anchors, and screw directly into a stud. If there's one close enough that it looks okay, you should do that. You'll have to patch up these holes, which may be a bit of a pain to do with the textured walls, but it's doable.
The next best option is probably to use a toggle bolt anchor. These are bolts that expand when you put them in the wall:
![alt text](https://i.stack.imgur.com/XBzUa.jpg)
This site has some good info on them, including a sizing chart:
Toggle Size Drill Bit Needed
1/8" toggle 3/8" drill
3/16" toggle 1/2" drill
1/4" toggle 5/8" drill
5/16" toggle 7/8" drill
3/8" toggle 7/8 drill
1/2" toggle 1 1/4" drill
This option has the advantage that you can probably use the existing holes (just use a large enough toggle bolt), and bolts are reasonably strong so hopefully this won't happen again.
It's hard to tell from the picture, but if the curtain hardware doesn't totally cover the holes you'll need to do some cosmetic work. Keep in mind though that if you patch these holes with compound, they still won't be as strong as regular drywall, so you won't be able to put the same size anchor back in and expect it to hold.
You're not showing all the pieces. What we see is a curtain rod and the center support.
There are brackets for the end that the rod hooks over.
Pictured is a dual curtain rod hanger bracket. The hole in the rod catches on the tang and it drops down onto the bracket.
The answer to your problem might be shown in the picture, use a nice board that spans across the window opening about six inches above. Use screws to hold it to the studs and then mount the curtain to that using stronger screws than came in the hardware pack. Graininess of the cellphone picture doesn't do the spar varnish finish on the hemlock board any justice.
For spanning that window (10') there are heavy-duty three piece curtain rods constructed exactly like these but with two of the screw-in supports available in addition to the end brackets.
![enter image description here](https://i.stack.imgur.com/WqqNG.png)
Best Answer
Agree with the comments above. No way those will hold the rail loaded with curtains for any length of time in drywall (I repair this kind of failure ALL the time, as rarely do things ship with suitable fasteners...).
You need a fastener which opens out on the backside of the drywall but it depends on the construction of the house. Whats behind the drywall? Timber frame or masonry?
I see you're in the UK, so it's likely the drywall is stuck to blockwork using an adhesive (dot and dab). In that case the second fixings would be better as it would get into the wall itself.
Drywall doesn't have good holding power unless you can get behind it using a fastener which opens out (not possible on 'dot and dab') or through it and into the wall.
NOTE: Where you have drywall bonded to masonry, use a 7mm or brown rawlplug and drill a hole deep enough to ensure the whole of the brown plug is in the masonry.
Typically this means a 8g or preferably a 10g screw at least 65mm or 2 /12" long.