It depends on what you mean by "most likely" and what you mean by "can trace." Wikitree has specific standards for labeling a father/son connection as "confirmed with DNA". Essentially, Wikitree has drawn a line and said "you can only put confirmed with DNA if you have passed a threshold of likelihood that they were father/son by meeting these standards."
You only have a paper trail connecting you to Francois through your paternal line, but WikiTree policy would not have you mark any of those connections as confirmed with DNA, because there is no proof that your Y-DNA actually came down to you through each of those connections, regardless of what the paper says. Sometimes, a family makes up a lie, and they stick to it so well that all of the paper records state the lie rather than the truth. You just can't know.
If you want to increase the likelihood that you and Francois have the same Y-chromosome, excepting probably a few mutations, you need to find another person who can reliably trace their paternal line back to Francois through paper records and compare your Y-DNA to theirs. If yours matches this agnate cousin, excepting a smattering of mutations, then people would say you are then much "more likely" to have the same haplogroup as Francois.
Just using the paper trail, the likelihood that your Y-chromosome matches Francois's all depends on how solid the paper trail is. With so many generations between you and Francois, going back to the 17th century, there is usually a connection or two that is less certain than the others. And again, sometimes the paper just lies. One of the good uses of a Y-DNA test is adding additional evidence to shore up those connections, but to do that you need to find a cousin to test and see if he matches you.
