France historically held about 180,000 troops on its Italian border. Even a partial redeployment gives French planners substantial reserves for the north, including the possibility of manning more blocking positions in the Ardennes. Occupied obstacles would force German combat engineers to fight through positions that were historically left unmanned. One additional division might impose the delay needed for the Allies to react, although French command could simply reinforce its existing dispositions instead. A failed or prolonged Norwegian campaign would also remove one source of confidence behind Hitler's gamble in France.
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French redeployment could close the Ardennes gap
Removing the Italian threat frees roughly half of the French troops guarding the Alpine frontier, and one extra division in the Ardennes might disrupt Germany's strategic gamble.