Under the 240-hour visa-free transit policy, the last country (or region) before entering the Chinese mainland and the first country (or region) after leaving the Chinese mainland must not be the same.
According to the itinerary you described — Geneva-Paris-Beijing-Paris, this route does not meet the requirements of the 240-hour visa-free transit policy.
However, if you travel directly from Geneva to Beijing without a stopover in Paris, and your itinerary is Geneva-Beijing-Paris, and you hold a British passport, then your trip meets the conditions for applying for 240-hour visa-free transit. Please note that the final decision is subject to on-site inspection and approval by the immigration authorities.