I have a valid Schengen visa for the Czech Republic for business. I now need to travel this time from my home country to France.
Will the same Schengen visa be valid?
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Assuming you have an unexpired multiple-entry visa, it's valid for any country in the Schengen zone, which includes France.
Assuming that the visa is for multiple entries, and that you've completed the trip to Czechia you got it for, then: Yes, you can use it for travel to anywhere in the Schengen Area without any further formalities.