The bid, valued at an estimated 34.2 billion euros (pounds 23bn) comes amid Societe Generale's bid to buy Paribas in a move to create Europe's second- biggest bank, which had left BNP looking vulnerable to a takeover.
The Conseil des Marches Financiers, France's stock exchange regulator, said BNP had offered to buy all outstanding shares of both banks.
BNP was offering 11 of its shares for every eight Paribas shares and 15 BNP shares for every seven Societe Generale shares, the CMF said.
According to the CMF statement, BNP's offer was conditional on its ability to acquire at least a majority of each bank's outstanding shares. The offer would need approval by BNP's shareholders of the issue of the necessary shares to carry out the takeovers.
The regulator said the BNP board had pledged at a meeting yesterday to submit the necessary resolutions to its shareholders.
The CMF has asked the Paris bourse to suspend trade in the shares of all three banks.
Societe Generale and Paribas surprised financial markets in early February by announcing a 15bn euro merger that would create France's largest bank and fuel the global trend towards fewer but larger financial institutions.
BNP has been under pressure since then to strike an alliance of its own, but has insisted it would not be rushed into a deal for the sake of a deal.
The chairman, Michael Pebereau, told a news conference this month that BNP, which unveiled a better than expected 23 per cent increase in profits last year, would consider "opportunistic" external growth if it created shareholder value and did not endanger performance goals.
The bid for Societe Generale is at a 14 per cent premium to its closing share price of 145.5 euros, while the premium to Paribas' share price of 85.95 euros is 24 per cent.