In fairness, Uffink qualifies his assertion as "true for the purpose of studying the conceptual structure of a physical theory". For historical purposes, Parisian scholastics and their successors, Oxford calculators, did pave the way for Galileo and Descartes.
Uffink most likely refers to the medieval theory of impetus, a modification of Aristotle's dynamics that replaced his antiperistasis theory of projectile motion mocked already in antiquity by Philoponus. The latter suggested that, according to it, one could make an arrow fly by waiving hands behind it. The idea of lasting "impressed force" (virtus derelicta), albeit decaying, anticipated the concept of inertia, see Who was the first scientist to suggest that objects can keep moving without applied force? and Why don't we learn Buridan's laws of motion?
The idea of impetus traveled from Hipparchus (allegedly), through Philoponus and then Islamic philosophers to medieval Europe, and more specifically to Paris first, see Van Dyck, Malara, Renaissance Concept of Impetus. There, Francis of Marchia and then, most famously, Buridan gave it the pride of place in their pre-modern dynamics:
"The introduction of the impetus concept in scholastic philosophy is traditionally ascribed to Francis of Marchia (first half of 14th century), who held the Franciscan chair
of theology in Paris, but recent scholarship has shown that there were some thirteenth century predecessors... Jean Buridan (1295-1363) formulated what has been called the "classical" concept
of impetus [13, p.134]. He quoted several empirical reasons to support the concept
of impetus and he also gave some proportional indications about how it relates to factors
such as the amount of matter that is put into motion [4, pp.521-523]...
Just as Marchia, Buridan also appealed to impetus in treating celestial motion, and he added acceleration as a further phenomenon that could be explained
by it. In the latter case impetus is not only the cause but also the effect of motion, as Buridan assumed that the body gradually acquires more impetus as it falls. Buridan’s direct successors, Nicole Oresme (1320-1382), Albert of Saxony (1320-1390) and Marsilius of Inghen (1340-1396), further took up the concept and offered treatments that afterwards spread over Europe from Paris."
I know that Marchia, Saxony and Inghen do not sound like Paris, but all three were professors at the University of Paris at various times (1320s, 1351-1362 and 1386-1396, respectively). Another name, not mentioned but associated with Paris and impetus, is Gerardus Odonis, see also Francis of Marchia's Virtus derelicta and the Context of Its Development.