The French champions appeared to be on the way to the three points in Friday's encounter at Stade Auguste Delaune, when last season's top scorer Zlatan Ibrahimovic broke the deadlock with a cool finish in the seventh minute.
However, the normally ice-cool Swede showed an uncharacteristic lack of composure when he somehow hit the post when faced with an open goal before he saw a 29th-minute penalty saved by Johnny Placide.
Reims capitalised on those misses as goals from Prince Oniangue and Antoine Devaux threatened to shock PSG and hand Jean-Luc Vasseur an unlikely win on his debut as their head coach.
It was not to be, however, as a costly error from Placide handed Ibrahimovic a second and PSG a point, but head coach Blanc was less than pleased with his team's finishing.
"We're not ready yet, and we could see it tonight," he told the club's official website. "Despite the result, I think my team played some very good football.
"We had so many chances to score, too many to count, including a penalty. We didn't kill the game off. We could have after just 20 minutes. We were expecting to struggle in certain areas."
Despite the disappointment of failing to start the campaign with a win, Blanc believes there are positive signs moving forward.
He added: "We didn't get the result we wanted, but it's still encouraging for the future."
