Protesters near the base on the outskirts of the capital Niamey shouted on Friday "Down with France, down with ECOWAS", referring to the West African bloc, which approved the deployment of a "standby force to restore constitutional order" in Niger, TRT World reported.
Niger's new leaders have accused ex-colonial power France, a close Bazoum ally, of being behind the hardline ECOWAS stance against the coup.
Many brandished Russian and Niger flags and shouted their support for the country's new strongman, General Abdourahamane Tiani.
France has around 1,500 personnel in Niger as part of a force battling an eight-year militant insurgency.
It is facing growing hostility across the Sahel, withdrawing its anti-militant forces from neighboring Mali and Burkina Faso last year after falling out with military governments that ousted elected leaders.
Niger's new leaders scrapped defense agreements with France last week, while a hostile protest outside the French embassy in Niamey on July 30 prompted Paris to evacuate its citizens.
AMK/PR