My My. This sure opens many cans of worms doesn't it?
Would the Brits try to force the Turks to give up on the Straits and give them off to more reliable Ally such as Greece in order to pull them to Allies? Or Perhaps Italy to sooth the relations of Italy in exchange of Italy becoming a member of British sphere?
Or would ensuring chaos give Stalin a margin of opening to try to seize the straits for himself with the Black Sea Fleet and a naval invasion that would make Churchill Blush?
or will a blockade be enforced blockade and a sanction that pushes Turks away from their neutrality?
And while I also can see nothing happening off of it at all. I doubt the League of Nations and Brits would be quite so willing to let the Turks to break the international rules quite like that with such a strategic location as Bosphorus straits...
The OTL Montreux Convention suited everyone, but that was a different world. Most of the main players are similar, Stalin isn't going to gamble on war with Turkey (not with the other Great Powers undistracted anyway...), the other Black Sea residents still want to ensure they have a guaranteed route to the Mediterranean for trade at least, Greece remains belligerent but not allowed at the table and Britain remains wary of setting unfortunate precedents, even more so than OTL - Having just used control of Suez and Gibraltar to seal the Med in the Abyssinian War the last thing they want is the League saying anything unfortunate about free passage rights and so on.
Turkey however is the wild card, pretty much everyone agrees with the Atatürk policy of neutrality and re-building domestically, but national pride and Turkey's position as a regional power are important, the OTL solution got Turkey that recognition through diplomacy. If there is no similar process TTL then when the Great Turk dies there is no guarantee İnönü will take over, at which point anything could happen.
Of course all that assumes the League doesn't force the issue earlier by noticing that Turkey has started re-fortifying the straits.
Also I'd like to add to your list of things to look up at is the various attempted deals and pacts Soviets and Finns tried to pin down one way or other. such as exchanges of Territory and various non-aggression pacts. As Finns do not want angry Russia, and Russia does not want a hostile landing ground for Germans in shape of a Finland.
it'd be interesting if there was some deal made that would avoid the Winter War and allow things such as Finns to sell few islands in exchange of few strips of land and a non-aggression pack.
the Horde of tiny islands as submarine hiding hole bases for Soviets might be quite traumatic experience for German merchant marine....
Interesting as that idea is, Germany only has half a dozen important convoy routes to run in the Baltic and they are mostly going to Sweden/Norway to bring in Iron Ore, Wood pulp and similar. Ex-Finnish bases would certainly put the Soviet sub fleet closer, and allow a lot more time on station, but aren't going to decisively change things. But it has been added to the idea database, so something may emerge.
As for the Winter War, I've not looked into it in depth but my feeling is that if WW2 hadn't broken out and there had been no Molotov-Ribbentrop pact then Stalin probably wouldn't have felt secure enough to attack the Finns. But that's more an instinct reaction than anything I've researched and thought about in depth.
All things considered. I'd almost half expect such alliance cause the Anti-Communist world to have quite an alarming wakeup call of OH SHIT COMMIES ARE SPREADING. And the Finns triple down on its frenzied search for support against Soviets. be it with a flimsy non-aggression pact. or attempt to get into Germany and British side for some form of Anti-Comintern support and military aid. Moreso, it might cause the Little-Entente to splinter between different factions which think IS neutrality keeping them safe or not...
All of that is probably the reason there will be no Franco-Soviet pact. I was toying with a "Only Flandin could go to Moscow" idea, that only someone on the right of French politics could make it work without setting off those alarm bells, but he probably couldn't. More importantly after the way the Rhineland Crisis went down in
Butterfly then it's arguable if either party is that scared of Germany anymore, at which point there's no need for such an alliance.
It would be interesting to watch the axis cannablise itself and try to form a super Germany or Italy out of its former friends and potential allies first before turning towards the actual otl targets east and west. Then again, you have to justify it in universe, and unlike me you can't just say a demon made them do it.
Then again, then again, the Little Entente might just mean Germany will try to do such things to Austria and Hungary anyway to try to get a grip back on a balkans it thought it had in the bag.
Germany will certainly attempt such things, after all you can hardly have a Großdeutschland without Austria. But remember Italy, Mussolini has lost his over-seas Empire, he cannot afford to lose Austria as well.
I chuckle and then think: little entente and france suspiciously left leaning might make people anxious. Romania moving towards communism as well (which it well might) and France electing a soclist governemnt will make the Axis lose their shit and freak out pretty much everyone else as well. Maybe even stalin, since everyone ganking france and then turning east in a unified alliance was certianly not what he was going for...
As it stands, from what I can remember the Empire is doing well/better than OTL. Italy is doing much worse after being thoroughly humilated and having its navy sank/taken by the former. Germany is ok but the rhineland incident made the nazis look a bit weak and manageable (which actually works against both axis and allies simultaneously) and they are blocked somewhat in the balkans by france as well. France is...weird. They did stand up to Hitler but this strained them quite a bit. They've pissed off Britian and had to make their own alliance in europe to make up for that. And socially, they might be even closer to going communist than otl, because of all of the above plus other things. Oh and they technically are fighting a proxy wat of sorts against the nazis and brits with the aid of the Soviets, all under the guise of helping chosen factions in spain.
...oh and there's some football and tractors in there for quite a bit. And the postal services of the world? Anyway, the general upshot is thst there are communists everywhere and everyone is very scared.
France luxuriates under a Centre-Right government, the Popular Front did not have a good 1936 election and so Sarraut remains Prime Minister of France, his centrist Radical party supported by the ARD and the rest of the centre-right. No-one is going to worry about France turning Communist anytime soon, though they should be worried about all sort of other things happening in France, mostly the things that also caused problems for the OTL Popular Front government.
Don't get me wrong I'm sure there are people shouting about Communists everywhere, it's just no-one is listening to them. If the Republicans win the Spanish Civil War and the PCF leap into power, kick out the French and form an alliance with Moscow, that's the time to start worrying about communists everywhere. A scenario that has people in Paris somewhat concerned.
one of the original plans with Finns and Russians that were drafted but never followed on at. was an exchange of some border territory in Karelia (mainly forest and woodland with few Finnish villages and towns that existed at the time there), in exchange of some of the larger islands in Gulf of Finland, that presumably were suitable for Submarine use. As most small islands in there are too small for more than a fishing hut on them, really.
Its quoted by many of Finnish nationalists as being a bit of a missed opportunity, as this deal was rejected by Mannerheim. H
Laws on coastal waters were a bit harsher back in the 1930s, if the Soviets got too many large islands could they have legally closed the Gulf of Finland just by enforcing their rights?
If not, then submarine use does sound the most likely explanation. Either way, an interesting corner of history.
) or a couple, if it’s the same length it still takes the same amount of time to read it. 
