yvesj--The following thread seems to offer a free service in recovering deleted Live Mail emails.
http://windowslivehelp.com/community/t/6280.aspx
You could try it. They do the work for you. I suspect you will have to register to be able to post on that forum. And of course the service may no longer be available.
If unsuccessful, you could try DBXtract. You have little to lose. If DBXtract works on Windows Live Mail, once you find the message you want, open Windows Live Mail. Does it have a View option on the Toolbar? If so click it and look for Layout. Click that and then check the box near the bottom for Preview Pane|Apply|OK. When the Preview Pane is open drag and drop the specific email file into the Preview Pane. You now should be able to view it in the normal way you view Windows Live Mail messages.