I don't see how the Dutch can resist for long on their own with the IJN and naval landing forces (and whatever Division or two or three the Army is willing to release from China or Manchuria). Anybody know what the numerical strength of all Japan's naval landing forces added up to in terms of Army Division equivalents?
I also anticipate an argument that bases in southern Indochina are vital for Japan to mount operations against the DEI, but I beg to differ. While land-based air from Indochina and ground and naval task forces staging from there in OTL's 1941-1942 offensive, looking at the arrows on the map, a lot of the DEI operations were staged out of Palau and the Mandates, and from Hainan island.
The shape of the offensive will look different, yes, Java and Sumatra would not be attacked in force at the earliest parts of the campaign, but the eastern DEI is fully exposed to the Japanese coming out of the Mandates, and it supplies ports and airfields to support consecutive rapid offensives to the west, culminating in seizure of Borneo/Kalimantan [not British Borneo], Sumatra and Java.
My initial instinct is to say that London and especially Paris, as outraged and frightened as they are of the sudden Japanese offensive in the Indies, are not going to be inclined to declare war on a Japan that does not attack their possessions or declare war on them. They will want to do so only with a commitment for the Americans to join in, which they will not get at this stage. [However, America will likely impose full economic sanctions on Japan in protest as soon as the 6 month post-cancellation period for the US-Japanese Trade Treaty is up, about late January].
It seems to me that without US naval support, France and Britain, expecting a showdown with Germany in the spring, and seeing the USSR as a second hostile and aggressive power in Europe, probably do not want to take on a third enemy in Asia.
On the other hand, some (including historian Gerhard Weinberg) have described Paris as being keen to expand the war to almost any place besides the Franco-German war and Belgium. That's the explanation some have for France's advocacy of aid to Finland or bombing Baku. If they are looking for an excuse to focus on fighting elsewhere, possibly Southeast Asia would do just as well. The Australians and Raj officialdom will be basically pressuring London to go this route too.
But presuming London and Paris decide to not fight Japan as long as Japan is not imminently attacking them, the British at least are going to beef up their Far East defenses and provide reinforcement. They will join in any American economic sanctions as well, although it is rather late for these with the DEI under Japanese control.
The French will not have any reinforcements to spare for Indochina (except perhaps from concession areas of China itself). The Australians will not be sending any troops overseas to Europe or Africa, instead they will be establishing defenses in the north and in Papua (and possibly would regard Malaya, Singapore and Borneo as parts of their non-overseas theater). The lack of Australian availability later on may increase what London asks of the Canadians and South Africans and the non-white empire.
Japan with the DEI will have some access to oil, but a freeze of their dollar and sterling assets will hurt, and force various adjustments and substitution measures in addition to a domestic tanker building programs. The Japanese will also be eagerly seeking a Neutrality Pact with the Soviets, and trying to negotiate away sanctions.
When they see the scale of German successes in the Low Countries and France, the Japanese could be tempted to broaden their aggression against the British and Americans and French in Southeast Asia to secure their LOCs, isolate China and gain a wider resource base to partly compensate for their trade and financial losses. The interesting thing about them doing this, is that since they will largely be coming from the sea, there's a serious chance to the French in Indochina and British in Burma to cooperate with China or in the worst case retreat to China while preserving some forces in East Asia.