What if the Normans focused on expanding their power base in France?

If the French kingdom under Charles the Simple or one of his successors had collapsed or fallen to the Ottonian dynasty a few decades after the land grant to the Normans, and said Normans had stayed in the region to consolidate instead of departing on conquests to England, Italy and the Holy Land, how would history be impacted?

Would the Normans have forged a kingdom to stand the test of time? Would England have stayed Anglo-Saxon, or would they have fallen to the Northmen? Would southern Italy have remained fraught between Greeks, Muslims and Lombards? Would the crusades have ever been successful without their input?
 
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