"A lot of his answers sounded like they were prepared by a lawyer," French said this morning on "This Week," telling ABC News he does not believe Wilson's story of what happened.
A grand jury that investigated the shooting for three months declined to indict Wilson, the St. Louis County Prosecutor's Office announced Monday.
French, whose office in Ferguson was destroyed in violent protests after the decision, said he thought the Ferguson Police Chief Tom Jackson should follow Wilson's example and resign.
"I think it's impossible for this community to move forward with him still in that role," French said. "I think at the St. Louis County police department level, there still need to be some people to answer for how the police responded to peaceful protests in August, which really escalated the situation.
"Frankly, the thing we haven't seen is a lot of government accountability. Not many people have taken responsibility for what's happened, and people are still waiting for answers and change," he said.
The alderman gained national notoriety in August for chronicling the protests that erupted after Brown was killed on social media.
He pushed back today on a statement by Capt. Ron Johnson of the Missouri State Highway Patrol that law enforcement could not have imagined the intensity of the protests that followed the announcement that Wilson would not be indicted for killing Brown.
"I don't think that's right at all. We've been talking for weeks about this, and that we really had a powderkeg here. And so for the county prosecutor to decide to release the grand jury announcement at night time, for the governor to pre-emptively call a state of emergency and call in national guard, yet no one deployed them to West Florissant or other areas that have been hit repeatedly by violence, it really showed a failure to grasp the situation and to handle it on the part of government," French said.
"And so the fires that we saw, that violence that we saw, was unfortunate. It is -- it really hurts our hearts," he said. "We've gone through a tough week here, but we knew that a lot of people were very angry and we knew a lot of people were coming from other places. So we should have been prepared for this."