The UK shipping industry also poured scorn on the notion, saying: "Building a huge concrete structure in the middle of the world's busiest shipping lane might come with some challenges".
But the foreign secretary's suggestion has largely been met with scepticism and ridicule.
The Daily Telegraph has been told that when Mr Johnson suggested building a second Channel crossing Mr Macron replied: "I agree".
Johnson did not mention the idea of a bridge explicitly in public and it was unclear if any detailed discussions had taken place.
Asked for its view, Downing Street reacted coolly.
"What was agreed yesterday, and I think that's what the Foreign Secretary tweeted about as well, is a panel of experts who will look at major projects together including infrastructure", he added.
"Our economic success depends on good infrastructure and good connections", Johnson tweeted. The more successful Channel Tunnel began construction in 1988 and was completed in 1994. Others pointed out that such a bridge would be incredibly expensive.
His proposal for a new airport on an island in the estuary of the River Thames estuary - immediately dubbed "Boris Island" - was rejected.
Reuters reported France's finance minister Bruno Le Maire told Europe 1 radio, "All ideas merit consideration, even the most far-fetched ones ..."
"It's a very very busy shipping channel we all know that and by and large the ships are separated. Let's finish things that are already under way before thinking of new ones".
"The United Kingdom and France have a long history of collaboration in delivering cutting-edge technologies", a joint declaration after the summit at the Royal Military Academy, Sandhurst.
"Building a 22-mile-long bridge across the channel would therefore not be without its challenges, especially as the largest ships now transiting the strait have a height above the water line in excess of 60 metres".