I judge that crossing the line means crossing the Equator, and you are right. Just before crossing the Equator the Captain and some other Officers leave the ship and then return dressed as King Neptune (hence the spear) and his royal family. Those who are crossing the Equator for the first time are sentenced by this court and then initiated in some way - one of these involves kissing the Royal baby on the belly button (one of the officers dressed up) who has normally been smeared with oil and grease for the occasion. All very weird, but happens on merchant ships as well and in other maritime traditions (not just the UK.). The orders of the red or blue nose are certificates given to sailors who are in Arctic or Antarctic waters for the first time. Over to you !
It used to happen on passenger ships, too. When my parents emigrated to South Africa on the old Union Line ship, they were sentenced by King Neptune. At the end of the process my mother was thrown into the swimming pool. As she was a near Olympic standard diver she managed to turn her tumble into a well executed dive which, apparently, got a big round of applause. I was only three months old so my sentence was having a dab of swimming pool water put on my forehead. Next question: Which is the only country in the world that has more registered cars than people?
Sadly there's not much connection between that and the Paris theatre in the question. It is all to do with ballet and horse racing.
Is the connection Stravinsky himself. The Rite of Spring. The Consecration of Spring was first performed at the theatre of Champs Elysees and the Rite has been played by the Epsom Symphony Orchestra.
Sorry to be so late responding but the connection is between ballet and horse racing - it's all in a name!