According to Alexandre Ganoczy's Calvin’s Life and Context, chapter 1 in The Cambridge Companion to John Calvin there is no scholarly consensus as to the extent of Calvin's involvement in Nicolas Cop's speech "made on the Feast of All Saints in 1533 at the opening of the academic year":
Who was behind this speech? Scholarly opinions differ. Some attribute
to Calvin merely an advisory role; others think that Calvin wrote the
speech himself; and others attribute to Cop, the Erasmian physician, a
time of private study and a competence in theology similar to the
young jurist. One thing is certain: Calvin felt solidarity with Cop
and was able to affirm his statements.
Ganoczy himself seems non-committal, as is Thomas J. Davis, Professor of Religious Studies at Indiana University. In John Calvin, he writes
Historical evidence is ambiguous as to the authorship of Cop’s
address. Some think Calvin wrote it, or at least had a hand in writing
Also in The Cambridge Companion to John Calvin, Wulfert de Greef in chapter 3, Calvin's Writings , is of the opinion that:
Calvin was involved in drawing up Cop’s address.
De Greef does not give any reasons for his conclusion, but a more complete account can be found in Calvin: A Biography by French scholar Bernard Cottret. He is of the opinion that, while the question remains "open", Calvin probably did not write the speech but he
participated in its writing and...he even exercised a friendly
influence over Cop...
In arriving at this view, Cottret notes that
Various intriguing indications show clearly Calvin's involvement at
Nicolas Cop's side. A fragment of this text in Calvin's own hand
exists in Geneva, while the complete version, corrected by Cop, was
henceforth located in Strasbourg.
In a footnote, Cottret adds:
It is probable, moreover, that the two known manuscripts are
themselves copies of an original draft of the text.
Calvin's friendship with Cop certainly did him no favours in the eyes of the opposition. After the speech, Calvin's room was searched by the authorities, who also took his papers, but the backlash from conservatives was not aimed only at him, and nor was it entirely to do with Cop's speech. Ganoczy again:
...the reaction of the opposition affected Calvin exactly as it did the
university rector: both found themselves in that constantly shifting
middle ground of loyalty to the church and a desire for reform. In the
eyes of the Sorbonne occupying middle ground still meant schism and
heresy. This radically conservative group was successful in regaining
the confidence of the king by December, 1533. He ordered the
extermination of the “damned Lutheran sects.”
The king referred to is Francis I (1515-47) who was initially relatively tolerant of Protestantism despite pressure from pope Clement VII in August 1533 to take action against "the Lutheran heresy and other sects infesting this kingdom". The pressure and incentives to take action increased, though, as Francis was also vying with the Holy Roman Emperor Charles V for the pope's favour in achieving "Christian unity". The French king, after meeting the Pope on the 10th of November in Marseilles, was able to proclaim a "diplomatic victory".
It wasn't until an unrelated incident in 1534 (see Affair of the Placards) that Calvin was forced to flee France altogether (note that Sproul is mistaken: Calvin did not flee France because of Cop's speech).