What was the world´s reaction to Gadaffi´s Chad war ?
https://en.wikipedia.org/wiki/Ouadi_Doum_air_raid
France shut him down, basically.
Nigeria vs Cameroon, Togo, & Benin is not quite the same, though.
Nigeria has tight links to Shell oil. If Nigeria kicks out Shell and engages with Rozneft while invading Cameroon, then expect a swift and overt French military response (particularly with the Presidential election upcoming) with hard diplomatic campaigning by the Elysée Palace to prevent the
Admiral Kuznetsov group from obtaining any logistical support anywhere between Cape Town and Jan Mayen Land. The French aim will be to defeat the Nigerian incursion, possibly with the backing of the rest of the African Union, but probably not to enter Nigeria or achieve régime change - though the possibility of breaking the state up to reestablish the ill-fated Biafran Republic or something similar might be a possibility, to prevent a resurgance of foreign adventurism in Lagos.
Given the Nigerian order of battle, I would expect such a French expedition to be successful. Nigerian forces have had problems with morale, equipment, mobility, communications, and C3I in facing off against Boko Haram, an irregular light-infantry insurgency entirely lacking in armour and air power. Against a first-world mechanised opposition with significant artillery support and air supremacy, while operating outside Nigeria proper, I would expect a very poor outcome for the Nigerian force. France has recently deployed forces to Mali to combat Islamic insurgents there - this is pretty much meat-and-potatoes stuff for the staff courses at St. Cyr.
I would have thought that previous US administrations (both Bush and Obama) would have at least funded an AU mission to oppose Nigeria and to "peacekeep" (a.k.a. dissuade any Lagos regime from deciding to try again) in the attacked countries, but I don't know if Trump would support that measure. There would be pressure from some Republican party figures and large donors - maybe starting with Cheney - anxious to ensure that money from Nigerian oil flows to those US firms and not to Elf or Rozneft, though bear in mind that it's not simple nationalism - Glencore holds a stake in Rozneft, and there is some unsubstantiated speculation that Trump himself may do so as well, which might shape a US response if POTUS allowed such a conflict of interest to affect his decision-making. There is always the possibility that a sufficiently opportunist Washington might see the possibility of conquering Nigeria similiar to 2003 in Iraq, only restricting its occupation to the oil-producing coastal region and allowing the rump of the country to remain embroiled with Boko Haram, although that woulld be quite the hardship for the bulk of the Nigerian population - but also that a sufficiently Russophile Trump might ask Putin to do the same thing.
China has in the last couple of decades had significant engagement with large civil engineering projects in Africa, and if the US, France, and the AU do nothing, will probably look at some form of intervention here - most likely would be the provision of equipment and cadre to one side or the other in exchange for future basing rights and a continuing presence in the country, as it is a long way away and China hasn't really tried to build up its forces to support that kind of power projection.