What are the documents/legal requirements (eg- any mandatory min/max amount of hard euros or cash) if I am visiting 4 countries - Netherlands, France, Italy and Germany in Europe, If I already have valid tourist schengen visa issued by France ?
There is no maximum, but if you're entering or leaving the EU with cash worth more than 10,000 euro, you are required to declare it at customs.
There is no minimum amount of cash either. As a third-country national you may be asked to show that you have "the means" to keep yourself fed etc. during your visit -- but those means don't have to be cash. A well-recognized international payment card ought to be sufficient too.
If they think you look impossibly scruffy you might need to let them escort you to an airport ATM so they can see you can withdraw a reasonable amount of money -- but if that becomes relevant, the entry interview will already be going quite badly. Generally your financial capability will have been assessed in the visa application process already, so there's no need to repeat that at the border.
How much money you will be expected to have access to is not fixed, but will be judged by your individual plans and circumstances. For example, if you have a prepaid hotel reservations and tickets for the entire trip there'd be no need to able to pay for that another time. On the other hand, if you get to the show-me-the-money stage at all, it's because they're already quite suspicious of your intentions, and then showing that you're prepared to deal with random emergencies (for example, missing a flight) will be a lot more helpful than having a bare minimum of means.
If you needed a travel or health insurance to get your visa, you need to carry a copy of the cover with you.
And if this is a second or later visit on the same visa, you will need an up to date/new travel insurance or health cover for this travel.
That is separate from the financial requirements as mentioned in the first answer.