For modern/metro apps, there's nothing you can do AFAIK. This is by design because Microsoft is stupid and doesn't allow modern and classic applications to communicate fully with each other.
Beyond that, the only thing I could think of is to make sure your filetype/protocol associations are set to pale moon. Open up the control panel and find the default programs option and select the option about associating file types and protocols. Make sure pale moon is associated with http and https.