John Wycliffe's views on this subject don't seem to be quite as straight forward as was portrayed in the movie you refer to, but he did tend in this direction more than those of his day.
We must begin by putting the question in its historical context: there was little debate at the time over the fate of baptized infants. The fate of unbaptized infants who died was more controversial. Many church fathers wrote that unbaptized infants would be damned, but Wycliffe was more cautious. Albert Henry Newman writes:
While he believed in baptismal regeneration, he thought it possible that God might save such infants as died without it, but denied that any injustice would be involved in case he should damn such. (Manual of Church History, 607)
William Wall says that Wycliffe "suspends all opinion" on the matter, and provides several direct quotes from Wycliffe:
When an infant of believers is brought to church, that according to Christ's rule he may be baptized, and the water or some other requisite is wanting, and the people's pious intention continuing, he dies in the mean time naturally by the will of God, it seems hard to define positively the damnation of such an infant; when neither the infant nor the people have sinned, that he should be damned. Where then is the merciful liberality of Christ? [...]
[I]t is not clear to me whether such an infant shall be saved or damned; but I know that whatever God does in it will be just, and a work of mercy, to be praised of all the faithful. (History of Infant Baptism, II, 164–65)
This is further than many church fathers were willing to go, but still not the same thing as "all those dying in infancy will be saved."
B. B. Warfield summarizes Wycliffe's view and connects it to that of his followers:
John Wycliffe (d. 1384) had already with like caution expressed his unwillingness to pronounce damned such infants as were intended for baptism by their parents, if they failed to receive it in fact; though he could not, on the other hand, assert that they were saved. His followers were less cautious, whether in England or Bohemia, and in this, too, they approved themselves heralds of a brighter day. ("The Development of the Doctrine of Infant Salvation," in Works, IX, p. 416)
Thus Warfield sees Wycliffe as taking cautious steps away from the traditional understanding and toward the possibility of infant salvation without baptism. His followers went further, and ultimately infant salvation came be accepted by some reformers (notably Zwingli) and from there more widely to Protestantism (for more on this, see Schaff, History, VII, 559–60).