"The girl is drinking milk."
Translation:La fille boit du lait.
"The girl is drinking milk" means that at the action is currently in progress and not finished.
In French, you cannot express an on-going action in the same manner, i.e. with a verbal form.
Therefore, either you use "la fille boit du lait" (simple present), but you miss the "in progress" nuance, or you use the expression "la fille est EN TRAIN DE boire du lait", which exactly means what is implied in the English "is verb-ing".