When I look up the website I've made for a customer (www.leadevreese.be) through "Lea De Vreese" I get an internal page, and not the home page.
How can I fix this?
It's very likely that Googlebot (Google web crawler) found your internal webpage before the home page (because of a link find in a website for example) and didn't follow links on this internal webpage to index other webpages of the website. In general, it's the case when the website is young and has few backlinks pointing to it.
To fix this, you can submit a sitemap.xml to the Google Webmaster Tools account managing the website and put links pointing to it over the web. Therefore, Googlebot will find it and will index the webpages.