According to my knowledge as i know if you have an Italian residence permit and non Eu passport, you are not allowed to live in Switzerland and work. As long as she has a valid Schengen visa/permit she doesn't need any additional permission/documents to travel in France.

She can travel in any Schengen area using her Italian permit without any problem. I have a friend who has the same permit and been frequently travelling to Spain.

Yes, she's not allowed to live in Switzerland without a Swiss residence permit (and of course not allowed to work). She is allowed to stay on visitor basis for a maximum of 90 days within any 180 day period. 

Should the authorities find out that she overstayed, she may be fined or even go to prison, deported back to Italy (as long as her Italian residence permit is valid) or her country of origin and may be forbidden to return. 

the question was about the travelling not working... let's focus.

(these people have never been to Italy or Spain to get this paper. Their employer helped them to got it by a lawyer, because they can work until somebody pays tax after them... if you are right we wouldnt see here any of them.)

Hello Gina,

With my first reply, I wanted to confirm Waqas's assumption. And in the same time provide additional information: this is a public forum, so other persons will read the thread and may be happy to find more info than just an answer to your question. And, btw, the "90 days rule" also applies for travel to France, so it may also be useful for the person you asked for.

I didn't and still don't want to "unfocus". However, again due to the fact that this is a public form, so other persons will read the thread and may get false ideas from misinformation on the thread, I must reply to your statement:

"these people have never been to Italy or Spain to get this paper. Their employer helped them to got it by a lawyer, because they can work until somebody pays tax after them... if you are right we wouldnt see here any of them."

I understand (and hope my understanding is not correct!) that "their employer" is in Switzerland and had an attorney apply for a Spanish respective Italian (in short: EU country) work and residence permit although it was never planned that the people should work in an EU country. The EU permit should just allow their holders to travel to Schengen - Switzerland so that they can work here.
I am not sure what you mean by "pay tax after somebody", but please be informed, that paying or not paying taxes has nothing to do with being authorised to work in Switzerland, and it will not allow anybody to work in Switzerland. Because:

No EU country permit allows a person to work in Switzerland.

I hope for the attorney that (s)he does not know about the scheme behind the applications for EU permits. Otherwise (s)he would be in big trouble if the authorities in the country of application ever find out about this (if the authorities work correctly) and likely also in Switzerland (above all in Switzerland if the attorney is based here). The employer (the feigned in the EU country and, first of all, the one in Switzerland) would be in any case... The illegal employees who surely had been misinformed by the employer and assume that all is ok may (if they're "lucky") "only" be deported and banned from Switzerland and the Schengen area, but this surely will be worse for them than the likely financial fines (Swiss courts seem to try to avoid sending people to prison wherever possible?) for the employer.