I believe what you are asking is how to build apps that use X11 on Macs. The program in question comes with Makefiles, which normally would mean they could be built on the command line.
But they have a lot of very specific things hard coded to the system the developer was using:
ifeq ($(DISTRIB), osx)
PKG_CONFIG = x86_64-apple-darwin15-pkg-config
CC = o64-clang++
#CC += -arch i386
CC += -arch x86_64
endif
Changing this to:
ifeq ($(DISTRIB), osx)
PKG_CONFIG = pkg-config
#CC = o64-clang++
#CC += -arch i386
#CC += -arch x86_64
endif
And then "make DISTRIB=osx" (in bellepoule-6.0-master/build/BellePoule) shows the following:
lauland@XXXX BellePoule % make DISTRIB=osx
Package goocanvas was not found in the pkg-config search path.
Perhaps you should add the directory containing `goocanvas.pc'
to the PKG_CONFIG_PATH environment variable
Package 'goocanvas' not found
Package 'libmicrohttpd' not found
Package 'libqrencode' not found
Package 'json-glib-1.0' not found
Package 'libzip' not found
Package 'webkit-1.0' not found
Package 'libwebsockets' not found
\e[1;31m Release/libbellepoulebeta.dylib \e[0m
ld: warning: ignoring duplicate libraries: '-lc++'
ld: library 'ssl' not found
So it requires quite a few other packages, just to start, and looks like probably more than just those. It might be possible to install these via homebrew or macports, but they may not all be available.
If the developer said you "just need to know how to compile", they probably assumed you were on Linux or Windows.