Let's just assume it's captured intact and not get bogged down by how it's captured.
The fleet at Mers-el-Kebir comprised 4 battleships and 5 destroyers. Combined with the Kriegmarine's 4 battleships, this gives Germany 8 battleships. The Royal Navy in 1940 has 14 battleships. Italy has 7 battleships and the Royal Navy needs to screen those so in actual fact there are only 7 battleships which can be used against the German invasion and we can't assume they're all in service. At least 2 will be under repair or refit so in actual fact the Royal Navy only has 5 battleships. The same won't apply to Germany since the French fleet would have been recently captured. So now Germany has 8 battleships vs Britain's 5. Those 8 battleships are enough to escort the troop transports crossing the channel and the continual flow of supplies. The Royal Navy won't risk an attack because it's outnumbered. Britain's aircraft carriers are counterbalanced by German air bases on French soil close to the channel.
The fleet at Mers-el-Kebir comprised 4 battleships and 5 destroyers. Combined with the Kriegmarine's 4 battleships, this gives Germany 8 battleships. The Royal Navy in 1940 has 14 battleships. Italy has 7 battleships and the Royal Navy needs to screen those so in actual fact there are only 7 battleships which can be used against the German invasion and we can't assume they're all in service. At least 2 will be under repair or refit so in actual fact the Royal Navy only has 5 battleships. The same won't apply to Germany since the French fleet would have been recently captured. So now Germany has 8 battleships vs Britain's 5. Those 8 battleships are enough to escort the troop transports crossing the channel and the continual flow of supplies. The Royal Navy won't risk an attack because it's outnumbered. Britain's aircraft carriers are counterbalanced by German air bases on French soil close to the channel.