Is it expected that the Pakistani Muslim young man's family would approve of his marriage to a European Christian girl if she converts to Islam, and what might their reaction be in that case?

It is difficult to predict the parents' reaction to their son marrying a foreign woman, but it is likely that they would prefer him to marry someone from their own country and close to their customs. They might fear Western decadence and their son drifting away from them. However, they might agree if the woman is a Muslim and righteous, especially if the son will settle in the West. Your conversion to Islam is commendable, whether you marry this man or not, for pleasing Allah by following His religion is more important than all other considerations.