I am an Indian national and travelling to France and Switzerland for 3 days each, and then to Croatia and Italy for 6 days each. My first destination is France and the last destination is Italy. Since I intend to spend the same time in Croatia and Italy, would I need to apply for a Croatian visa as well?
Croatia allows holders of still-valid Schengen visa with two or multiple entries to enter Croatia without applying for a Croatian visa.
You seem to imagine that this rule only applies if you would still have applied for the visa from a different Schengen country if Croatia had already been a Schengen member. But there is no such restriction.
When you apply for a visa for the Schengen part of your trip (from the Italian consulate, since that is your main destination within the area), document the entire trip. You should end up with at least a 2-entry visa with a duration-of-stay of 12 days or more, and that will be enough for you to enter Croatia between the two in-Schengen parts.