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If your website doesn't render correctly on mobile devices, you need to consider whether you make it responsive, dynamically serve content or build a parallel mobile version.
1. Google recommends webmasters follow the industry best practice of using responsive web design, namely serving the same HTML for all devices and using only CSS media queries to decide the rendering on each device.
2. Dynamic Serving: server responds with different HTML (and CSS) on the same URL depending on the user agent requesting the page. The contents of the response will vary depending on the user agent that requests the page.
3. Parallel mobile version: each desktop URL has an equivalent different URL serving mobile-optimized content. A common setup would be pages on www.example.com serving desktop users having corresponding m.example.com pages serving mobile.
For more details in French: http://www.mozalami.com/strategie-mobile-seo-3-options-2013/