Can I extend my Schengen visa from France in Italy?
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As a US citizen, you can stay visa free in the Schengen area for 90 days out of every 180 days. You need a national (D) visa for any longer stay.
Days spent in the nation which granted your D visa do not count against the 90-day limit. If you were in France for most of the last six months, you probably have some visa-free days left.
You cannot extend your French visa in Italy. You can in principle apply for a new Italian D visa. For details on that, ask in Expatriates Stack Exchange.