Last month, trade unions and members of the Yellow Vest movement led a raucous crowd to the historic Le Centorial building, where BlackRock has its offices, lighting flares and denouncing what they said was an effort to impose American-style free-market rules on France.

There is no evidence that BlackRock influenced Mr. Macron to push retirement savings to it or any other financial giant, although financial firms could get some business from part of the pension overhaul that encourages high earners to invest in stocks.

And BlackRock strenuously denies the claims. “We deplore the fact that our company continues to be caught up in an unfounded controversy driven by political objectives,” it said in a statement. “We reiterate that BlackRock has never been involved in the current pension reform project and does not intend to be.”

Yet BlackRock’s role as an adviser to governments and central banks and as a major shareholder in some of the world’s biggest companies has quickly made it a symbol in a country that has long been deeply skeptical of capitalism and the stock market. The social climate here has grown more tense after recent nationwide strikes to protest the pension overhaul.

BlackRock has tried to portray itself as an industry leader in responsible investing. The protesters on Monday cited BlackRock investments in the French oil giant Total and the construction company Vinci as running counter to that.