Unfortunately, we do not know exactly when the first season of Fall Guys ends. All we know is that it will end on October 6, 2020. As you can see on the screenshot (taken on August 17, 2020), the developers are just telling us how many days there are left until the end of the first season. At the time of writing this is 49 days (October 6).
However, it may well be midnight on October 6, 2020. As a rule, developers end the season around the world at midnight. Again, this is just a guess, because because of the pandemic it is quite possible to move the second season.