Such questions are better for asking consular and border services. I will add, ą $ practice shows that in case of the first entry on a French visa to Bulgaria (if the visa is still valid in full), there should not be any problems with entry to France.

But in the next once visas in the Visa Center of France can reasonably be asked the question: "Why this open French visa was repaid at the first visit by the Bulgarian border guards?"

It's better to make an initial visit to France on an open French Schengen visa.