When you first log in to a Babbel app, you will see the following message – Babbel would like to Access the Microphone. Choose Allow, follow the instructions given and speech recognition will then be ready to use.
If you choose Don't allow, but later change your mind, this can be easily fixed. Just tap on the microphone icon in any lesson that includes speech recognition and you'll see instructions on how to Allow access.
You'll find the option to adjust the microphone sensitivity in the app's settings.