The arc will only remain available after that time if you've unlocked the first goal, All Wet.
When you get to Paris to try and get access to Vivian Vandermeer's fashion show in order to get back The Golden Monkey of Papeete, you find Michigan Smith already waiting for you.
He urges you to stop what you're doing. When you brush him off, he gets even more upset.
During the conversation, you can either decide to tell him you're going backstage for 2 or say you'll figure something out. The rest of the goal will be a little different depending on which option you choose.
If you choose to sneak backstage, you'll meet fashion designer Nina Westley, who is very surprised to find you there, but is excited to work with you. This will unlock the goal Treasured Runway.
If you choose to figure something else out, Michigan will again try to make you reconsider, but when you don't budge, he'll tell you not to sneak in and bid on the monkey. Confusingly, he'll give you 500. This will unlock the goal Down, But Not Out!
Dialogue[]