This exact issue happened to me, and I searched for hours to find a solution.
The one that worked for me can be found here;
It's essentially a different link to download the Valorant client. I know you may be wary clicking random links off the internet, but I took a chance and it actually worked out.
Once you download the file next to "Install:" on that thread, just double click the Valorant installer and you're set.
Hope this helps! 🙂