Williams had hinted that Dan was in line for a starting role after Chris Paterson had failed to find his top form in Scotland's opening games against Wales, England and Italy.
Williams said: "The obvious question is who else can play in Chris's position and I'm hopeful of Dan Parks' future.
"He showed tremendous signs in attack and in his kicking playing for Glasgow and in the very limited opportunities he's had with the national side.
"We've been impressed with him at training and he's improving greatly.
"But the step from professional rugby to the national side in Scotland is enormous and against France, who I believe to be the best team in the world at this moment, it's a huge step.
"We have to make sure that Dan is ready when he's chosen to make that step and we thought we might be rushing him into a very tough arena.
"We have a strong plan in place for the next 10 months when Dan will get plenty of opportunities but we thought it best if he started this game on the bench."