Good evening Vicki and welcome to the Events Calendar Support forum!
Thank you for reaching out to us.
I would love to help you with this topic.
If you haven’t already, my first recommendation would be to go through the following guide: https://theeventscalendar.com/knowledgebase/setting-up-the-events-calendar-with-wpml/
Normally (if your setup is correct), the french version of the calendar should be located exactly like you have described it (http://www.mywebsite.com/fr/events).
As a first troubleshooting step, could you please provide us with your system information in a private reply ? (following the instructions found in the link)
And while you are at it, would you please try the option Use directory for default language in you WPML setup ?
Best regards,
Geoff B.