I am building and as the norm requires me I put in place a communication box. I would like to know how to connect my livebox to be able to distribute Internet and the tv by internet on all taken rj45 of the house
First of all, the best would be to question your ISP... Except that the Wifi passes badly in your home, I do not see the interest of using the RJ45 sockets. If you really want wired, why not use a modem-router, plugged directly into the high-speed phone line. That being so, you are pushing me to a place far away from DIY... I advise you to ask the question on our forum or on the one of our friends at commentcamarche.net.
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