Though I doubt most people will be as idiotic as we were, I thought it'd be worth a post to stop anyone else walking in to the Conscrits hut for the first time learning the hard way.
Above the Tre-la-Tete refuge, the new high path to the hut is not signposted at all. If you take the main path from the hut, in about five minutes you'll come to a signpost for the Tre-la-Tete Glacier and the Conscrits hut, at a sharp right switchback along a short slabby bit of rock. Do not take this path but instead continue straight ahead along the unsigned path, following spray-painted blue dots on rocks and cairns. Alternatively immediately above the Tre-la-Tete theres a faint path breaking off left, which also takes you in the correct direction and rejoins the main path a bit higher.
The signed path is the old path via the glacier, and is infeasible. It's also relatively easy in poor visibility and a blasé attitude to nav to convince yourself you're going the right way due to the frequent cairns. The path ends at an improbable but possible-looking gully with some signs of footfall. If you have gone wrong and find yourself here, backtrack and take the correct path. Do not be tempted to take the gully - it is loose beyond belief and incredibly dangerous. The only positive to it that it does eventually intersect the path and doesn't end in an impasse - but you'd be lucky to make it up without having a serious accident.
Just a friendly warning for any fellow idiots