Here's the ukgov website on asylum applications. It's pretty clear you should apply when you enter the UK, not before. Nothing in there about filling in forms or showing your paperwork at any time before you get here.

https://www.gov.uk/claim-asylum

Your solution seems to make it harder for them to get to the UK and seek asylum by adding in more hoops to jump through (get to Paris, fill in an application, provide documents, etc.). Pretty sure that's both illegal and not going to help stop human trafficking.