First of all, France did not support Biafra militarily. The support was humanitarian and had little impact on the direction of the war. And it wasn’t just the Soviet Union who supported Nigeria, the British too were with Nigeria. And the sympathy of NATO members is emotional at most and has no bearing to their national security or welfare.
If the US had supported Biafra it wouldn’t have been militarily. It would have been more diplomatic, in that they would pressure Nigeria to tone down the war and pursue a quicker resolution with the Biafrans? It wouldn’t be military support because,
1, It will conflict with their British allies who are openly in support of Nigeria. Why annoy the Brits for a black region?
2, There is nothing to gain from independent Biafra that they cannot get from Gowon’s Nigeria. And dealing with Gowon, a man of limited education would have suited them more than dealing with Ojukwu a graduate of Oxford.
3, They were already neck-deep in Vietnam. Adding Biafra into the interventionist map was not something they wanted, nor can afford. Leaving Vietnam was the priority.
4, Communism was the number one enemy in the American foreign policy. If Nigeria was a communist state and the war was ideological then America would have been more interested.
5, Economically, the US wouldn't want to lose in the war. US private arms dealers were selling ammunition to Nigeria, why should the US interfere with the trade? The Biafrans could buy if they had the money, perhaps, but there is no need changing the platform from a marketplace to an aids-place.
6, Ideologically, it will contradict American history having fought and kept their country together the century before.
That said, assuming, for the sake of assumption, the US supported Biafra militarily, will it have affected the outcome of the war? Of course. That wouldn't necessarily mean victory for Biafra. These are what could happen (in present tense):
1, The US must convince the UK to back out of Nigeria. They won’t want to come against their biggest ally at the West African battlefield. The British will not take this lightly and two things will happen:
a) The British will insist and make US abandon the idea.
b) America will buy the UK over and it will cost a ton of political currency.
2, With England out of Nigeria, the US will put intense pressure, privately, on Nigeria to let Biafra go.
3, If Nigeria refuses and it will take a lot of balls for them to, the US will go public, condemning Nigerian genocide in Biafra and begin to make noise about war crimes. Next, they will recognise Biafra and urge the world to do so.
4, With the recognition of America the secessionists will have a big morale boost as many more countries like Israel, Australia, Canada, West Germany etc will recognise Biafra.
5, The Soviet Union will feel slighted and urge Nigerians on, they will intensify bombing in Biafraland.
6, The US will enter the war fully.
i, The US will get Cameroon open their border and America will ship in food and medication and ammunition.
ii, They will bomb Federal positions in Enugu, Onitsha, Port Harcout, Calabar and Owerri.
iii, They will bomb Lagos, Ibadan, Kano, Kaduna etc and let the Nigerian populace feel the heat.
iv, Biafrans will most likely recapture Port Harcourt, Onitsha etc, yes, with US fighter-jets harassing the troops it will be easy.
7, The battle will be deadlocked as the USSR won’t give up.
8, The matter will go to the UN. Remember the issue was never mentioned in the UN floor because the UK kept blocking it. But with Biafrans and Nigerians exchanging fire for fire and swapping trucks of corpses, the world will be forced to act and call for political resolution.
9, Nigeria will eventually let Biafra go. Discontent will lead to a coup in Nigeria, and new head of State Murtala Mohammed who was disgraced out of the Onitsha Sector of the war will bring an end to the war, blaming Gowon for it.
10, The US will eventually back out at a change of governance. I am assuming that Badass Lyndon B. Johnson brought US into Biafra let’s say in mid-1968. With Nixon in power in January 1969, he could say ‘what the hell are we doing in Africa?’ and pull the support. Then Nigeria will regain the upper hand pre-US involvement. Or like Vietnam, ol’ Nixon will escalate the war, not wanting the red devils beat the US for whatever, on anything.
(It will be hard to see which one happens first, number 9 or 10, and it depends on how far the US and their communist rivals are ready to play).
11, Or, the two African countries will get tired and end hostilities and resolve to cold war like North-South Korea. Some white dude will get Nobel Peace Prize for it. There will be a US base in Biafra and heavy Russian tanks in Nigeria.
12, Reconstruction will be stronger in Biafra as the US will want to justify their involvement by building a strong economic state. Tension will remain till the end of the cold war. Fancy Reagan escalating tension in the gulf of Biafra. He may visit Enugu, Biafra and say, ‘General TY Danjuma (Nigerian new head of state) if you want peace, if you want growth, if you want prosperity tear down the bridge of the evil empire of Communist Russia.’
All these are hypotheses, of course. I strongly doubt the US would have ever entered the war. And none of these eventualities above is granted. The US might successful negotiate an end without firing a shot. Or out-muscle Russia or the USSR will bully them out. Who knows?