If this is going to be your first visit on this visa, you should cancel your visa and apply for a new one. There is no way to change your visa from one given out by France to one given out by Italy.
For second and later visits, it does not matter which Schengen countries you visit and how long you stay in each, as long as you remain at most the number of days allowed for each visit and at most 90 days in each 180 day period. (Additional restrictions may apply and will be mentioned in the visa if so.)
How easy it will be for you to travel with the 'wrong' visa does depend on your nationality and how difficult it is for people from your country/in your circumstances to get a visa.
It is in the entry interview on coming into the Schengen zone that you will be asked about your plans. If you can keep it vague, some days in France, some days in Italy, they might accept it.
If you had to supply details for all hotels and all internal travel, you better not change the visa by so much. In the entry interview they will want to see details and will not accept such a change, might send you home without allowing you to enter.
On the other hand, if you are one of the lucky people who get a visa with very little information needed from you, you can take more risks. Officially you are not allowed to do the change you plan, but you will likely not be asked about it. In that case the interview will likely not go into details but it still can. Never lie to immigration officers but being vague or not having detailed plans yet might work.
Best is to change your plans back to stay in France the longest, so your plans match your visa again for the first use of your multiple visit visa, for later visits you can visit any of the Schengen countries unless your visa specifies countries you are or are not allowed to enter. (Which is very rare.)