Ok, problem solved 
My initial PATH
/usr/lib64/qt-3.3/bin:/usr/local/bin:/usr/bin:/bin:/usr/local/sbin:/usr/sbin:/home/jdoe/.local/bin:/home/jdoe/bin
It can be split into three files
/etc/profile.d/qt.sh
Code:
if ! echo ${PATH} | /bin/grep -q $QTDIR/bin ; then
PATH=$QTDIR/bin:${PATH}
fi
I reversed the order here.
/etc/login.defs
Code:
ENV_PATH PATH=/bin:/usr/bin:/usr/local/bin
ENV_SUPATH PATH=/usr/sbin:/usr/bin:/usr/local/sbin:/usr/local/bin
note that if you do not mention ENV_PATH in the file, the default (as per the man login page) is "/usr/local/bin:/bin:/usr/bin".
Note too that documentation seems to conflict on default paths between login and login.defs.
/etc/skel/.bash_profile
Code:
PATH=$PATH:$HOME/.local/bin:$HOME/bin
You might have move options in /etc/profile.d.
You might also have more options in ~/.bash_profile
My result:
Code:
/bin:/usr/bin:/usr/local/bin:/usr/sbin:/usr/local/sbin:/usr/lib64/qt-3.3/bin:/home/jdoe/.local/bin:/home/jdoe/bin
Thank you all for your help.