Paris to Stuttgart: would like to spend time in Italy on the way.

Italy is not on the way to Stuttgart. Stuttgart is on the way to Italy.

As you said, it's a little late in the planning, but you can fly between Florence and Stuttgart. I've flown the Florence to Stuttgart route, very small plane, close to the tops of the mountains. You might check into flying from Paris to Florence and then from Florence to Stuttgart.

Pay attention to the weather. It is winter and it will be cold and wet and snowy, maybe in all the places you mention. That and the short days will affect where you can go and how you can get there.

I am working my way from Paris to Stuttgart....... I would really like to stop in Italy on the way there

How are you traveling?

Where do your flights arrive/depart from?

It definitely cold and wet and snowy. It’s winter! I have been to Europe two times in the winter as it’s cheaper and less crowded. I am totally fine with it.

To Joe: I am looking at flying from Paris to Milan. I found a flight for $35 on east jet. I am going to use planes and trains. I am too intimidated to drive, haha.

Also: I guess I could go Paris to Stuttgart to Italy, but does it matter? (Genuine question)

I have to fly in and out of Paris. That was my sky miles deal. Not ideal, but...that was the deal. :)

I guess I could go Paris to Stuttgart to Italy, but does it matter?

Where are you flying into and where are you leaving from? The best plan is to do an "open jaw" flight, into one city and out of a different one. Then choose a few locations between them and "join up the dots" on a map.
If you have to double back that costs time and money.

Paris to Stuttgart is ~3½ hours by rail. Stuttgart - Florence and Paris Florence are both a lot further and you would need to fly, unless you want to stop off in Switzerland on the way.
And, two weeks from now is the first half of February, the coldest time of the year. Ask your friend what the weather will be like in Stuttgart. Florence is further south and will be warmer.

For both rail and air, you are booking at relative short notice, so the cheapest fares have all been sold.
for Paris-Stuttgart look up times and by tickets on: https://www.bahn.com/en/view/index.shtml

I think you need to look at a map, and do some fast decision making. And enjoy yourself.

It won't give you all the answers, but for planning sequences of travel, I tend to use Rome2Rio website. It will list mode of travel options, but keep in mind the prices vary and are not dynamic, so may not take into account seasonal reduced services or pricing.....but it does show potential length of time and price ranges. From there, you can check the reality on the specific train or plane website.
Sure, it is harder to do outdoor things in the winter, but you are surrounded by heated buildings and can add layers. Don't let that dissuade you.
You could easily spend the 5 days in Florence, but there are day trips to Piza, Lucca or maybe one of the spa towns like Montecatini Terme and indulge 'in the waters'.

Great advice. Thank you!