Paris Fashion Week -- Is it impossible to get into a show?

You can try and request invites from the smaller independent designers, or you can try and stand in line the day of to see about getting in. All the bigger shows will have their seating arrangements made and confirmed within weeks of the show, unfortunately.

Something to keep in mind, but you do need the (printed) invite to attend the shows. Since you noted that you'd be traveling, you should try and have them mailed to your hotel. It sounds like many folks have gotten theirs in the post already.

Good luck!