"free adaptation" is a correct and usable phrase in written English.
You can use it when you are talking about the process of altering something to better fit a current situation or context. For example, "The director used free adaptation to bring this classic novel to the big screen."
I'm cooking my way through Noodle! by Mimi Aye and hope she'll forgive my free adaptation of this dish.
Not that Heiner Müller's 1980 play, a wildly free adaptation of "Les Liaisons Dangereuses," isn't verbal as well as visual.
His complex and idiosyncratic harmonic system was a free adaptation of 12-tone technique, which he called the "mother lode".
Even though the names remain the same, this is apparently a rather free adaptation, newly set in the Deep South.
The funny bunny was not the only arrestingly peculiar image in this brash, aggressively violent and very free adaptation of Shakespeare's tragedy.
I think I can see why Jonathan Kent has chosen to use Brian Friel's very free adaptation of Turgenev's 1848 classic.
Jack Pulman adapted Robert Graves's wonderful novels I, Claudius and Claudius the God – themselves free adaptations of the Lives of the Caesars, by the 1st-2nd century AD biographer Suetonius – and the writing is elegant, grown-up, cliche-free.
But Omar has become famous in the West through the very free adaptations by Edward FitzGerald of his robāʿīyāt.
Until the Reformation, Dutch Bible translations were largely free adaptations, paraphrases, or rhymed verse renderings of single books or parts thereof.
Later, Edward FitzGerald aroused new interest in Persian poetry with his free adaptations of Omar Khayyam's robāʿīyāt (The Rubáiyát of Omar Khayyám, 1859).
In most of Dürer's free adaptations the additional influence of the more lyrical, older painter Giovanni Bellini, with whom Dürer had become acquainted in Venice, can be seen.
