I've seen you have 35 languages in your site. Please consider that WPML needs to run the code and do database calls for each language you have in your site, so a high CPU usage might be expected in your case.
I'm afraid the only options in your case are either to reduce the languages or update to a higher performance server.
I don't have any mean to check, since I can't access the site and your hosting profile (and I would advise you not to share hosting credentials).
Please provide some data. Do you have any slow queries? Duplicated ones? Does anything change removing all plugins except WPML ones? Where do you see the high CPU load?
I'll enable private reply for credentials but from the WordPress backend there's little I can do. You should talk with your hosting to see exactly where such spikes come from, but increasing resources might be the only solution.