Mr Kouchner called for quicker changes to the peacekeeping force
The HRC expressed concern over reports of torture, discrimination against women and the use of child soldiers.
It also condemned violations in Darfur, including murder, rape, evictions and attacks on civilians.
In a separate development, the French foreign minister called for quicker deployment of a joint UN-African Union peacekeeping force to Darfur.
In its first overall review of Sudan's record for more than a decade, the HRC said "widespread and systematic serious human rights violations, including murder, rape, forced displacement and attacks against the civil population, have been and continue to be committed with total impunity throughout Sudan and particularly in Darfur".
The HRC, which comprises 18 independent experts, called on Khartoum to "ensure that no financial support or materiel is channelled to militias that engage in ethnic cleansing or the deliberate targeting of civilians".
The AU peacekeeping force currently in Darfur is over-stretched and under-funded, the BBC's Elizabeth Blunt in the Ethiopian capital, Addis Ababa, reports.
The current plan is to move in phases towards a properly resourced and full international peacekeeping force.
In the next phase the AU will reinforce its troops with logistical support from outside, and only in the third phase will this become a hybrid AU-UN force.
France's Foreign Minister Bernard Kouchner said this process would have to be speeded up, and UN funding would be needed for this.
"We have to join, to merge, the third phase with the second phase," Mr Kouchner said, speaking in Addis Ababa after talks with AU and Sudanese government officials.