I am wondering if it is bad for SEO to do this since Googlebot will probably fall on 'fr' or 'en' but not both.
Since you don't know where a certain bot comes from and you have no guarantee that the bot location will never change, it may lead to confusion. If the bot will be seeing a different version now and then it may decide a page is too volatile for it to have high rankings. Anyway, only Google people could tell you what the implications are.
Also not do it this way that the url of the home page stays the same but the content is served in different languages. Each version should have its specific url and that should be fixed.
Would it be fixed if I add a link inside my page to the different language page.
It will help the localized urls to be discoverable and keep their rankings. Your initial home page may however have bad rankings or none at all since it will only be redirecting and to a random location each time.