Hello Sophie,

I was able to translate your homepage using this guide:
http://support.themely.com/forums/topic/how-to-translate-about-section-content-in-integral-theme/page/3/#post-1215

You will want to go to String Translation section:
http://maralavocat.apps-1and1.net/wp-admin/admin.php?page=wpml-string-translation%2Fmenu%2Fstring-translation.php&context=admin_texts_integral

Than you can fill the Services setion just like the one above. You should tick the desired row, change its main language to French (there is a button just below this section), then fill the correct Page ID of the translated page. In your case, the services pages are:
– English:400
– French:389

Please give it a try and let me know if there are any problems.

Cheers,
Piotrek