Greetings,
This might not be possible today as allowing Azure Front door to inject the client certificate into request header: X-ARR-ClientCert similar to App Services is not yet implemented and is been under triaged.
I would recommend you upvote this feature in the feedback section. All of the feedback you share in these forums will be monitored and reviewed by the Microsoft engineering teams responsible for building Azure.
Please do not forget to "Accept the answer" wherever the information provided helps you to help others in the community.