International Schools in Lausanne Area Question?

Hello, everyone!

This is the first time I write in this forum... but it is for a quite relevant issue for my family ;-) We are moving in January from Madrid to Lausanne due to my new job there, and we are currently looking for a school in the Lake Area (from Nyon to Montreux). We are thinking in an international school, since my children(11 and 14) speak with English but almost no French, and since I have understood there are quite good schools there (even the State ones).

What I have to ask you is... what schools would you recommend to me in the area? And also if you can help me in understanding which kind of students my children could have in their classes (more Swiss or more expat profile... and this kind of things).

Thank you very much! I hope you can help me!