Since the header.php and footer.php files are pure PHP and not parsed by Unicity CMS, if you wish to use modules within these files, for example to include a menu, they have to be written in PHP instead of using Unicity shortcodes.
Each module has an index.php file which must be loaded using include_once, for example for the module sectionmenu:
include_once("modules/sectionmenu/index.php");
Then to use the module, call and print the function with the name of the module, passing any parameters (comma separated, as with any PHP function):
print( sectionmenu( 1 ) );