ENTERTAINMENT 11/09/2018 04:32 pm ET At 6 months old, the little royal tends to shy away from the spotlight. By Carly Ledbetter Prince Louis-sighting alert! The 6-month-old makes a rare appearance with his mother, the Duchess of Cambridge, in a BBC One documentary about his grandfather, Prince Charles, which came out Thursday. The audience only gets a brief glance at Louis in “Prince, Son and Heir: Charles at 70,” but his chubby little arms and cute outfit are sure to make royal fans swoon. The last time the public saw the prince was at his christening, when he was joined by most of the royal family, including the Duke and Duchess of Sussex, dad Prince William and siblings Prince George and Charlotte. His six godparents also attended the ceremony, which was followed by tea at Clarence House. Prince Louis Arthur Charles was born on April 23 at St. Mary’s Hospital in London. Just hours after his birth, his parents stepped out together to introduce their son to the world. Louis is currently fifth in line to the throne, after Charles, William, George and Charlotte. Louis recently gained a new cousin, as Pippa Middleton gave birth to her first child with husband James Matthews in October. They welcomed a baby…