Thank you so much for sharing your question about filling in the curtain rail holes. I suggest using Selleys 180g Spakfilla Rapid Gap Filler. Make sure to check and remove any loose paint flakes around the area before applying the Spakfilla. Please give it enough time to cure before adding another layer or sanding it down.
If you're painting it the same colour save some of the large paint chips and bring them to the store for a colour match. I recommend getting Taubmans 250ml Sample Pot White and a small paintbrush.
Here is a handy guide to help you repair the holes: