Reportedly, the junta publicly claimed that the French troops were involved in preparing to militarily restore the deposed president. (As they said nothing of the kind about the US troops, we're left to infer they claim this was mainly a French plot.)
putschists accused France of planning strikes to try to free Bazoum. They also accused France of planning a military intervention in the country, an allegation denied by France’s Foreign Minister Catherine Colonna. On Thursday, the broadcast of French media RFI and France24 was suspended in the country.
As for less stated reasons, the BBC points out that the tone of the French and US public diplomacy differed too:
after President Emmanuel Macron's vocal condemnation of the 26 July coup and his public support for Mr Bazoum, still detained in his presidential residence, Niger's new military rulers opted for a radical change of policy, demanding that the French pull out. [...]
Yet while France and the EU are cold-shouldered, with Paris blamed for problems and crises of almost any kind and even accused of supporting a 2007 rebellion by Tuareg separatists, the US retains a significant presence, sending a new ambassador to Niamey in August. [...]
Paris, and indeed Brussels, have also paid a price for their strong support for Ecowas.
The bloc's 2001 democracy and good governance protocol is the foundation for its uncompromising stance towards the coup leaders and its efforts to pressure them into taking steps towards the re-establishment of elected government, with Niger in particular targeted by a trade blockade and the threat of military intervention.
Yet Ecowas itself is widely unpopular, often portrayed as a presidents' club that has turned a blind eye to election rigging and constitutional manipulations as heads of state seek to extend their stays in power.
[...] the US has played a softer-toned public game. It waited many weeks before finally acknowledging the overthrow of Niger's elected government, which automatically, under American law, triggered the suspension of most development aid.
With a generally favourable or neutral image in West Africa, where it has no colonial history and the Cold War left no painful conflict legacy, Washington has been able to sustain diplomatic engagement with the military regimes in a way that Paris could not have done without a humiliating disavowal of its core policies and track record.
Setting an assertive tone, [Nigerien] Prime Minister Mahaman Lamine Zeine said on Wednesday: "If the Americans want to stay here with their forces they should tell us what they want to do."
Mr Zeine was not shy to hint that Niger has other suitors and alternative friends if the US does not play ball. Russia's Deputy Defence Minister Gen Yunus-Bek Evkurov visited Niamey earlier this month. [...]
However, Niger's military rulers also face awkward dilemmas. While overtures from Russia and declarations of solidarity from Burkina Faso and Mali provide a degree of political comfort, the humanitarian and security realities are grim. [...] since the coup, a combination of Ecowas trade sanctions and the suspension of much development aid, has sharply worsened living conditions for many households and jeopardised long-term development programmes.
And after many army units were redeployed to Niamey to guard against a potential Ecowas military intervention, there was a marked upsurge in jihadist attacks and inter-communal violence elsewhere in the country.
So, the US approach somewhat more resembled how they e.g. handle disagreements with Israel, i.e. tried to give the Niger junta some slack, at least in public.