*I bet if you put 1000 words of content about medecin generaliste paris on the landing page you'd get closer to your competitor!
*Internally link to your landing pages using real and helpful anchor text (negative and positive anchor text)
*Your using a .com address. I notice that most the SERPs on google.fr are .fr domains. I have the same issue on google.co.uk with .com / .co domains. I've found including the country name in the page title and h1 tag helps.
*Google Webmaster Tools also has a geographical target zone, set it to "France" (I've never noticed a massive impact from doing this - but it can't hurt).
*Keep building links to this page AND THE PAGES LINKING TO IT
And yes, your link Metrics are better from what I can see. But your competitor might just have more content on their pages?! And your domain is over 11 years old!