That is a tight, but legal connection. United and Lufthansa do share the same terminal, although it is rather a sprawling thing. I am assuming that this is all on one ticket and that your luggage is checked through. If this is the case, you have a decent chance. If this is two separate tickets, try and get your luggage checked through.

You have to clear immigration - i.e. The Schengen border in Frankfurt, your hand luggage will clear customs in Frankfurt, but you probably won't notice as the process is just walking through the appropriate channel. You will have to clear transfer security, as you are on a very tight connection look to see if your flight is cleared for the fast track channel. If it is, use it. With a 50 minute connection, you will not have time to dawdle, shop or have a look around, check the Information Display for your gate number as soon as you arrive, follow the signs and head straight for your gate. Your luggage will be transferred to the Paris flight and will be collected and pass customs there.

Should you miss your connection, then as long as this is one ticket, Lufthansa will put you on their next Paris flight that has available seats.