Generally, Microsoft .NET ClickOnce applications can be only started using Microsoft Internet Explorer. The application start-up fails on clicking on a such a link in Firefox. I came across a plug-in for Firefox that implements a work-around for this problem. I have tested it and it works as expected.
On clicking in the launch link, the Opening dialog from Firefox is displayed. The section "What should Firefox do with this file?" contains a new entry:
- Run ClickOnce Application
On selecting it and confirming with OK, the ClickOnce application will be started properly.
You can download on the official Firefox Add-ons page.