Thanks for the bump Richard 😉
Finally found a solution tonight :

Step 1
——–
Debian :
sudo apt-get install quota quotatool

CentOS :
sudo yum install quota

Step 2
——–
Edit /etc/fstab
On the partition line, write these options : defaults,usrquota,grpquota

Step 3
——–
unmount then mount the partition again with this command (for the / partition, if your setup is different, modify the command accordingly) :
sudo mount -o remount /

Step 4
——–
Create the necessary files (/aquota.user and aquota.group) with the following command :
sudo quotacheck -cvugm /

Step 5
——–
Edit the quotas for the user wou want to limit as you see fit :
sudo edquota username

Step 6
——–
Once you’re done, save the file and activate the quotas :
sudo quotaon /

This worked on both my CentOS and my Debian 7 lab virtual machines. 🙂