Witch trials only really started then yes, for the Mediaeval Church largely thought it a fantasy. It has to do with the breakdown of the spiritual world, the Church rent asunder, that people thought Satan more active.
That said, burning of unrepentant heretics happened throughout the mediaeval period, notably of course the Knights Templar and the Albigensians. Witch trials are just a specific flavour of this.
The Renaissance has no relation here, as witch hunting was largely a popular practice and the rediscovery of Pagan texts was not. Besides, the Renaissance starts with figures like Petrarch, and at different times. Why on earth would Old pagan immolation to Taranis and such, be adopted anyway? The only thing it has in common is burning. No, any relation here is far-fetched.