But are they formal heretics?

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I see Bishop Williamson is asking the wrong question, too.  No one cares if he's a formal heretic, and no one is arguing that he (Francis or any of his predecessors) is.  It suffices that he is manifest.  If he's material and manifest, then he's not pope by virtue of that fact alone, since material manifest heretics (e.g. your average protestant) aren't Catholics (that is, they don't belong to the Church) and you'll find not a single Catholic source who says they are-- in fact, they all say they aren't (see the extant thread Matthew started about judging sedevacantism for thirty pages of crickets trying to find anyone who taught that material manifest heretics are Catholic).  In fact, Catholic theologians don't even entertain the idea of a "Catholic material heretic."  The term (material) itself pertains only to non-Catholics because the material/formal distinction indicates one's guilt before God, not one's membership status in the Church.  One can belong to the Church and be guilty before God of any number of things, and one can be outside the Church and not be guilty of being outside the Church (but can of course, and virtually always will be, guilty of something else, since a preponderance of grace is available through the Church which will be ordinarily unavailable to all of those outside her). 
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Just more fuel for the committed sedeplenist and rabidly anti-sedevacantist tire fire, I guess.  Good shepherd, huh?  At least y'all won't get cold :)

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But you're missing the boat, too, Jpaul.  Formal heresy doesn't matter to us.  It matters before God, not before us, and not even before the Church.
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There's a man, and he can be two things: he can be Catholic, or not.  We're using the strict sense here: Catholic means "a man who belongs to the Church" and non-Catholic means "a man who doesn't belong to the Church."
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A man, however evil, can belong to the Church if he professes the faith (and a few other things which aren't really debated, like whether or not he's baptized).  A man can be a hypocrite in professing outwardly when he does not so inwardly, and still belong to the Church.  A man can privately eat babies and belong to the Church.
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A man, however ill or well-intentioned, who does not publicly profess the Catholic faith, cannot belong to the Church.  How can he rule her, then?
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Everyone wants to talk about material/formal and it.just.simply.doesn't.matter.  We're not trying to figure out where, if Francis, were to die this instant, would go for eternity.  We're trying to figure out whether or not he is simply capable of ruling the Church-- not whether or not he can do it with courage or with cowardice or with a love of Christ or a hatred of Him-- but whether or not he can do it at all.  Do do it at all he has to be Catholic.
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I think what you're pointing at, Jpaul, is the fact that modernists are like Arians.  They're slippery and they're slimy.  One of the main heresiarchs, Eusebius of Nicomedia, was present at councils with Arius and his role was quite literally to translate for Arius any time he got "too Arian."  It's important to heretics that they be viewed as faithful.  So in that sense it's true to say that the modernists will hesitate to "define" error-- they don't believe in error in the first place, because they don't believe in truth.  You can't believe fully in a thing if you don't fully believe in its contrary.  And I'll give you as much to say that it's certainly worth keeping in mind that modernists do not announce themselves as such (not usually, anyways-- Francis pushes that envelope), so a sort of hyper-vigilance is required to be on guard against them.  But that doesn't answer-- it doesn't even touch-- on whether or not the man is pope.  And if someone doesn't want to touch that question, fine.  St. Paul instructed us to flee from heresy and as far as I'm concerned that's enough to justify the flight.
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But if you're going to try to get involved in the discussion of sede vacante, at least get your opponent's position right.  Somehow sedevacantists have managed, among the billion sedeplenist arguments on the planet, to realize that the infinitesimal minority which composes the SSPX (for instance) actually believe differently than what Walter Kasper, or Josef Ratsinger, or Karol Wojtyla believes.  Extend the same nominal courtesy to us and address the point, please?  Address our arguments, not those silly ones that are so easy for you to build out of straw and burn down while you all slap each other on the back.

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I see Bishop Williamson is asking the wrong question, too.  No one cares if he's a formal heretic, and no one is arguing that he (Francis or any of his predecessors) is.  It suffices that he is manifest. 
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You are wrong. Sedevacantists may not care if Francis is a formal heretic or not. But not all traditionalists are sedevacantists. You don't speak for all traditionalists.

My point being that one does not have to meet a canonical and legal standard to be recognized as a heretic by other Catholics. And a heretic is objectively outside of the Church.  One is cast from the communion of the Church by doubting but one point of Christ's doctrine.

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Indeed.  Ergo, we see that Christ responded to doubting Thomas, "Be not faithless but believing."  Thomas didn't apostatize; he held the whole faith-- except for one doctrine.  And he didn't deny it, either.  Just doubted it.  But that single doubt of just one teaching made him "faithless."