I personnaly think that there should be a big mistake on our site that penalize us and our SEO but I can't find what it is...
You are correct. Your site is duplicated. It appears as both www.proximeety.com and proximeety.com. Both versions of your site have links as well, so your link juice is divided between your two sites. You need to decide which version of your site you prefer, the www or non-www version, and then redirect traffic to ensure only one version of your site is in use.
Also, your home page has 15 internal links and 82 external links. That profile is backwards. Most of your links should be internal with a few external links added as appropriate.
In short, your home page needs major SEO attention. I would advise hiring a SEO professional as it seems to need a complete overhaul. If you wish to perform the work yourself, the Beginner's Guide to SEO is a great place to start.