Do you believe at the end chapters 1-6 in Book the Third of A Tale of Two Cities that Darnay is finally safe from the revolution?

No.  Keeping in mind that Dickens's novel, A
Tale of Two Cities, is a narrative of parallels and doubles, the trial of
Darnay in Paris parallels that of his trial in England.  For, just as Stryver has played
to the crowd in creating doubt regarding the identity of Charles Darnay as the man who
passed treasonous papers, so, too, does Darnay play to the sympathies crowd of French as
he aligns himself with the prisoner of the Bastille, Manette, and as the loyal friend
who returns to save a citizen's life.  Of course, both these instances illustrate the
corruption of the justice systems before and after the revolution, pointing to the
underlying problem as that in human nature, a problem that will
continue. 

Therefore, because of the fickleness of human
nature, as well as the vengeful force of Madame Defarge, who has knitted the name
of Evremonde and all relatives into her death cloth, Charles Darnay will surely answer
for "the sins of the father" and be retried again by the fickle tribunal of
the bonnets rouges the Jacques) that also seek
redress for all the injustices dealt them by the aristocracy.  As another parallel, in
Chapter II of Book the Third, there is an incident that recalls the metaphoric Chapter V
of Book the First that presages the French Revolution's bloodbath as the grindstone that
sharpens the blades of the guillotine emerges with the hideous and frenzied faces of
those who turn it madly drink much as the frenzied residents of Saint Antoine drank
the spilled cask of wine,

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As these ruffians turned and turned, their
matted locks now flung forward over their eyes, now flung backward over their necks,
some women held wine to their mouths that they might drink; and what with dropping
blood, and what with dropping wine, and what with the stream of sparks struck out of the
stone, all their wicked atmosphere seemed gore and fire. The eye could not detect one
creature in the group free from the smear of blood. Shouldering one another to get next
at the sharpening-stone were men stripped to the waist, with the stain all over their
limbs and bodies; men in all sorts of rags, with the stain upon those rags; men
devilishly set off with spoils of women’s lace and silk and ribbon, with the stain
dyeing those trifles through and through. Hatchets, knives, bayonets, swords, all
brought to be sharpened, were all red with
it.

This parallel to the
spilling of the wine casket in Book the First in the company of the other parallels
mentions suggests very strongly that Charles Darnay will, as his mother feared, have to
answer for the crimes of the family Evremonde.