TLDR: Start the download in Firefox then cancel it. Open the download page (Ctrl+J) right-click the download and select "Copy Download Link" then use that url with wget.
I was also having this same issue.
After looking into this issue I found this Reddit thread. Towards the bottom u/RelativisticTrainCar responded saying that you can copy the download link from firefox.
I was attempting to download "Pokehaan Craft" from this link.
What I noticed is that the link provided from the direct download link provided on the page was https://www.curseforge.com/minecraft/modpacks/pokehaan-craft/download/3154263/file
However, when I used curl I noticed that it was attempting to use Cloudflare to validate that I'm not a robot and of course this was unable to pass this validation which I assume is why wget throws a 403 forbidden message too.
Using Firefox I use the aforementioned link to start the download and open the downloads page (Ctrl+J). I then right-clicked the download and selected the "Copy Download Link" option. This provided me with https://media.forgecdn.net/files/3154/263/PokehaanCraft-1.1.2-ServerFiles.zip
This shows that curseforge is now using a CDN to provide file downloads. This CDN link works perfectly with wget.
So while it is a pain to do it this way, it's a guaranteed way to use wget to download straight to your Linux box rather than downloading using a browser and then Filezilla to push it to the box.