"We've got to concentrate on ourselves before we even contemplate other results," said Scarlets centre Davies.
"I don't think it would be a bad championship if we finished with three wins. But we know that we can do much better, and the way we've played in parts I think deserves four wins."
He added: "It's going to be a tough game for England going to Ireland, who played very well against us, but we've got to make sure we do everything we can before even thinking about winning the Six Nations. If England win, it won't even be an issue."
Wales, who have only claimed a top-three Six Nations finish twice since the tournament's inception in 2000, will face a French side reeling after last weekend's shock 22-21 defeat against Italy.
But Davies added: "They will be looking to rebound after the Italy game, but we have got to make sure we go there with the confidence we've built over the last three games and try and impose ourselves on them."