Neither the hosting support nor the Contact Form 7 support couldn´t help me with the issue. So I had to perform a lot of trial and error tests and I solved the issue and I want share the solution with you, to document your Knowledgement Database and allow other clients and / or yourselves know the solution.
The problem is that the JS of the Contact Form interferes with JS of the Google ReCaptcha. So disabling the reCaptcha is solved. If reCaptcha is necessary, generate new keys and activate it again.
