"We have spent a lot of time analysing Stade Francais. I have been over to see them a couple of times and done a lot of work on them," Williams admitted.
"My feeling is that they are the best team in the world right now. I think they would beat anyone. I think they would beat the (Canterbury) Crusaders.
"I can't see anyone getting close to them and right now they are in also in great form.
"But I always love coaching against the great sides. I have been fortunate to have coached against Auckland at their best and Toulouse when they were at their best. We had a good rattle at them and beat them.
"We have got nothing to lose on Saturday. The odds are going to be unbelievably against us.
"They don't like leaving France. They certainly don't like coming to Belfast. I certainly hope the weather gods put on a great Ulster night for them."
Weather aside, Ulster gained a timely first win of the season last Friday when they edged Edinburgh 13-9 in the Magners League and Williams has been encouraged by the response from his players after they started the campaign with four straight league defeats.
"The players are trying their guts out and they are performing. With all due respect to Edinburgh (by half-time) we probably should have been two or three tries up and then it is a different game.
"We just need that belief and I thought the crowd were brilliant on Friday night. And we need them again on Saturday against Stade, who will be a team to come and watch."
The Australian insists that Ulster will throw everything they have got at Stade.
The province, who have not qualified for the Heineken Cup's last-eight since they lifted the trophy in 1999, need to pick up points in their home games, two of which (Stade Francais and the Scarlets) are before Christmas.
"We've just got to really have a go at Stade. If we just sit back and play a kicking game, they will do you. They'll do anybody.
"But no side is unbeatable. They are an extremely good side with great individuals. Teams have pushed them but they have got through them in the Top 14. But this is a cup tie situation and they have to show it."
Williams is expected to have a near fully-fit squad to choose from. Winger Simon Danielli is a long-term injury victim, but Ireland international Paddy Wallace is set to return from a hamstring injury.
There is also a question mark over who will take the team's place-kicks, as Clinton Schifcofske has yet to hit form.
If fairness to the Australian, he has been nursing an ankle injury, but he landed only three out of six kicks against Edinburgh and Williams could hand the kicking responsibility this weekend to Niall O'Connor, Ian Humphreys or Wallace (if he makes it).