Thank you for posting, Jean_philippe
From what I can see, the payment for your new Photography plan has not been completed yet. Because the plan is currently awaiting payment, Lightroom is unable to verify the subscription, which can result in the Error 10000 message you're seeing.
Please sign in to your Adobe account and update your payment method, then retry the payment:
Manage your payment information
You can also review instructions on how to update your payment method here:
Retry a failed or missed payment
Once the payment is successfully processed, your new Photography plan should become active, and Lightroom should be able to verify the subscription normally.
Please update this public discussion thread if you continue to see the error after the payment is complete, Jean_philippe. ^JW