OK. This is going to be a bit messy, but I'll throw a few ideas out here that I haven't really had time to polish. The analysis claiming it's a draw hinges upon two key ideas:
(1) France cannot win without taking Ber and Mun or at least one Italian home center.
This is not true - France can, after all, win perfectly well by taking Warsaw or Moscow.
(2) France can never take Munich
This is also not true, albeit it's slightly more complex. But, as an example, if France were in Ber/Kie/Ruh/Bur/(Pie or Pru), France will be able to take Munich, at risk of losing Berlin during the same turn. These sorts of positions get extremely complicated, and it's perhaps worth analyzing one at some point, but for the moment I'll just make the point that it's not impossible from here that France would eventually get Munich.
Both are immediate threats -- France can convoy Kie - Lvn this turn (and I'd certainly order that if I saw F StP(nc); F StP(sc), and of course Munich is immediately under heavy attack, albeit not with a fifth unit in play for at least another couple of turns.
Moreover, there's an important flaw in the coalition's position which makes it very nearly untenable: you talked about at the very least being able to pull back to a stalemate line, but what line are we talking about?
An absolute minimal line to hold Munich involves 6 armies and a bunch of very carefully-placed fleets, but France can already prevent that line from forming -- those lines also require units (can be fleets) in Prussia and Livonia, after all. More realistically, it's going to take 8 armies to stop the French in their tracks. Where are those 8 armies going to come from? And, again, note that if France gets an army into Prussia, and he very likely will, then it's game over anyway -- your line is now drawn south of Munich.
Ah, but there we have a problem. Russia has but 6, one of which (Sweden) can be barred from getting into the right position. It's not at all clear that Trieste can be dislodged either; there's a good chance that it will end up being part of the line around Italy. Certainly the 4 around Munich are completely frozen in this position if Munich must be held. Moreover, by the time Russia loses Scandinavia, it will be down to just 7 units.
Turkey can spare a couple of armies, but of course the problem is that these armies need to go into places like Warsaw and Moscow -- those surely have to be occupied, but also occupied by Russians, or else the armies around Munich will be forced to disband anyway. Turkey can keep building armies as it takes over Italy, so even knowing a couple will be needed over there isn't a problem, but the problem is that it's really Russian armies, not Turkish armies, that are necessary here.
Can this be fixed? Yes, perhaps. In a press game, as Turkey I'd give Russia a couple of centers, letting him build armies, then take them back popping his fleets for the units I need in the Med. We might even be able to coordinate a trade in which I get my armies into Mos/War while Russia takes something to compensate. In a gunboat game, that's very unlikely to happen without any sort of miscommunication, though, and an accidental bounce, even if both sides understand and accept each other's intentions, can be disastrous.
Another option would be getting Turkish armies to be the supports around Munich. However, the Russian armies there are already pretty much locked into place, aren't they?
So, for the reasons I mentioned above, the position is probably dead if the coalition just plays for a stalemate line. This is why it looks like a win for France to me. Can we create counterplay?
Maybe. France's three fleets aren't quite sufficient to hold forever around the Med, and if Russia can somehow sneak a fleet, say, into the MAO and then Western Med while France is guarding his home centers, then Tunis can be regained with good coordination and timing. Alternatively, the situation in the north isn't entirely clear to begin with -- France will eventually win with infinite time, but if Russia makes a good guess in the coming game year and gets another build, plus a French disband, then perhaps Russia will win that war instead. Unlikely, but neither side has a 100% line, and the best French lines around Munich mean that he should probably not include BAL in his northern tactical planning; it's really in the Ber/Mun theater or convoying to Prussia or convoying to Livonia. I'd probably order BAL C Kie - Lvn immediately upon seeing F StP(sc), but otherwise it would go to Prussia, as that's almost certain not to be bounced, then I'd convoy the followup army Kie to Livonia with support in the Fall. At which point I'm past every line you want to hold, and so your only chance is making me disband before I can press home the win.
So then I guess the game hinges upon Russia doing one of two things successfully.
One would be building an army now, hoping to replace a dislodged fleet with an army, and racing for Pru/Lvn. France cannot both attack Munich with power 4 and race for Pru/Lvn, and so outguessing him about 3 turns in a row would give enough time for newly built armies to mean that Russia wins that race. That does mean outguessing France as to whether he's going for Mun or Pru/Lvn several times in a row, though, and being wrong even once means Russia loses. Turkey has to be very adept at figuring out where things are headed and responding accordingly here, too.
The other is hoping to find a way to win French centers immediately this year, and that the resulting disband will blunt the French attack. France does have one unit that can be easily disbanded (A Mar, though I'd prefer that in Pie) and another (the third Southern fleet) that can be disbanded in a pinch, as under this plan France might manage to win without Tunis if in return Russia is building fleets and France can throw armies into Pru and Lvn. But if Russia adds his own army builds to French disbands, then the game is probably drawn. This seems unlikely from the current position -- much more likely is that France can find a way simply to exchange centers evenly in the North this year, plus pick up Ber, throw F Bre on the board, and then win. But, it's not impossible -- if Russia guesses French orders correctly, Russia can definitely make progress.
So where does this leave us in total? I'm sure I've been a bit sloppy in a few places, but I really, really like France's chances of a solo from this position, and they likely become 100% if Russia and Turkey don't do something very intelligent immediately on the coming turn. At the very least, there's absolutely no way I'd have been setting my draw flag. And, if I saw a fleet build, I'd have been very confident that they weren't going to find a clever defense.
I think to some extent what I'm saying is that there are a couple of things you should always be aware of with stalemate positions.
One is that they usually require pretty precise play. Yes, in principle, Munich can be held from the south, and there are positions I can show you in which that's the case. However, those positions usually require not just the right set of units around Munich, but a bunch of other things as well, and a power in position to disrupt those other things is also in position to prevent that line from being held.
The other is that one major advantage that the power aiming for a solo has is that their units are truly interchangeable, while the opposing units are not. Even if there were no diplomatic problems with doing so, in this position Turkish armies cannot be the ones holding Mos/War because that would result in Russian armies disappearing to be replaced with Turkish ones many moves away from the front where they're desperately needed. Of course, this also means that France should be very careful here not to dislodge a fleet in a game year where he's not also taking a center, lest it be replaced with a much more useful army back at home.
In this particular position, both of these features come into play. Russia can hold Munich, but cannot hold a line that includes Munich, and Russia and Turkey have the wrong combination of forces to actually assemble a stalemate line. The combination means that in practical terms, I'd expect France is likely to win from here with strong play, even though I don't quite think it's a forced win.