How can I display Font Awesome fonts in Character Map?

You can use Character Map. Select the font and select Character Details

Character Map > Character Details

To find your character, use the view View > By Unicode Block. In All you have a very large list and in this list, you should find your character. But the font has 10FFFF (111411210) characters. Without knowing the code, it's a little bit hard to find your needed character.

You can also filter it out so it only displays the glyphs/icons specific to this font. Go to View > Show only glyphs from this font.

view menu in Character Map