Cascade de Flumen was the last waterfall we visited on our 2012 France trip, and it was certainly one of the more obscure ones because it probably wouldn't have had an obvious trail (or even be found) had a hydroelectric facility not been here.
It sat at the bottom of the head of the Flumen Gorge where we saw three misty waterfalls (each probably at least 30m tall) gushing in parallel. It was difficult to take a photo encompassing all three waterfalls, but then again we might have been here in flood (as evidenced by parts of the trail being inundated by the stream and the quantity of spray being blasted in our direction).
Perhaps what made this waterfall that much more intriguing was that there were other waterfalls (each with different names) further up the gorge, which we were able to see while driving the twisty D436 road between Saint-Claude and Septmoncel. I believe all of these roadside waterfalls along this stretch of road fed into the stream responsible for Cascade de Flumen.
We managed to take a trail from a hydroelectric facility near Le Martinet (an outskirt of the cliff-hugging town of Saint-Claude; see directions below). Even though the sign indicated it was only 20 minutes walk along the Flumen Stream to the waterfall, it definitely felt much longer than that.
The trail along most of the Flumen Stream was mostly flat and it looked like it used to be an old unsealed road. Signs pointed the way to the waterfall when there were trail junctions (except for maybe one junction where a trail went up but didn't indicate where it was going). In any case, it seemed like the road was there for hydroelectric purposes as it led to some bridge with some hydroelectric structures right on the stream.
When the trail reached that hydro-looking bridge, a smaller more narrower foot trail continued along the Flumen Stream to the right. Typically, that trail would've led us right to the Cascade de Flumen, but given the flooded conditions that the Flumen Stream was in, the trail was actually inundated and not safely passable (it was the kind of situation that could've easily resulted in getting swept away by the stream had we persisted).
Fortunately, there was an alternate trail that went up then closer to the waterfall before steeply descending in front of the waterfalls (thus bypassing the dangerous flooded section). And after having a difficult time trying to take photos without damaging our gear and not getting too soaked, we were back at the car after a little over an hour away from it.
From the town of St Claude, take the D436 towards Geneva. There will be a turnoff on the right down a decline towards the hamlet of Le Martinet (Road D290 or the Route du Martinet), which you take. After a few minutes on this road, be on the lookout for a small sign on the side of a building indicating Cascade de Flumen on your left. That sign will lead you on a very narrow (practically single-lane) unpaved road with a few ruts and potholes towards its end where there's a hydroelectric building and room for a few vehicles.
The trail begins behind the barricade next to the parking space. and heads in the upstream direction.
The trailhead was about a 90-minute drive away from Prévessin-Moëns (and slightly longer to Geneva). The waterfall itself belongs to the Jura Department of the Franche-Comté region (also known as le pays qui respire or the country that breathes given the region's laid-back and very "un-French-like" personality).
For geographical context, St Claude was 83km (90 minutes drive) northwest of Geneva and 128km (over 90 minutes drive) northeast of Lyon. The city of Lyon was 466km or at least 4.5 hours by car from Paris. However, we used the very fast and efficient TGV (high speed train or le train a grande vitesse), which wound up taking around 3 hours to cover this stretch between the two major cities.
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