A French foreign affairs ministry statement "strongly condemns" the violence and loss of life on Monday and called for "human rights and basic freedoms, starting with the right to demonstrate, to be respected".
It also called on the DRC authorities to exercise a "proportionate use of force to maintain order".
Six people were killed when police broke up a demonstration called by Catholic groups against President Joseph Kabila remaining in power.
UN observers were also threatened and molested by security forces.
The French statement called on the DRC authorities to find out who was responsible and bring them to justice.
Kabila's second term of office ended on 29 December 2016 and it should be his last, according to the constitution.
But the next presidential election has been set for 23 December 2018.
France has called for the timetable to be observed and said it is ready to "support the electoral process with a view to leading to peaceful and democratic change".