As part of a great skiing trip in France by train, I'll be getting a sleeper train into Gare d'Austerlitz at around 6am, then heading across Paris to Gare du Nord to get the Eurostar back to London. Given the time available for the transfer, I'm not planning to hang around at Gare d'Austerlitz, but instead catch the metro across so if there are problems there's time available to go a different way. (We got from Oxford to Bourg St Maurice without delays, in a relaxed trip, while everyone flying was delayed by a day, so karma may mean we hit problems crossing Paris...!)
If everything goes to plan though, I should have about an hour in Gare du Nord before the Eurostar checkin closes. I'm wondering if there's anywhere at/near Gare du Nord where I could get a shower? (I'll have access to the Business Premier Eurostar lounge in case that helps)