UK Prime Minister Boris Johnson has called on France to agree to "take back" people who cross the Channel to the UK.
UK government officials are due to attend talks in Calais later.
And Home Secretary Priti Patel will meet her French counterpart this weekend to discuss future cooperation.
Patel and French interior minister Gerald Darmanin will hold talks in Calais on Sunday.
Wednesday's incident marked the biggest loss of life by drowning in the English Channel on record and included 17 men, seven women - one of whom was pregnant - and three children.
In his letter to Mr Macron, the prime minister outlined five steps he wanted to see taken:
deploying more advanced technology, like sensors and radar
reciprocal maritime patrols in each other's territorial waters and airborne surveillance
deepening the work of the countries' joint intelligence cell
immediate work on a bilateral returns agreement with France, alongside talks to establish a UK-EU returns agreement.
"An agreement with France to take back migrants who cross the Channel through this dangerous route would have an immediate and significant impact," Mr Johnson said.
Johnson's suggestions, however, "will be hard for France to swallow" the BBC's Paris correspondent Lucy Williamson said.
On Thursday, Ms Patel told the Commons there was "no quick fix" to tackle the issue but said she had spoken to her French counterpart to offer to put more officers on the ground and had continued to push for joint patrols of the Channel.
She said it was important to address "long-term pull factors" and stop criminal gangs who treat people as "cargo".
But Calais MP Pierre-Henri Dumont dismissed the idea of joint patrols as "crazy" and said it would not change anything along the vast shoreline.
Darmanin said regional prosecutors had launched an investigation into aggravated manslaughter after Wednesday's loss of life.
He said two survivors were in a critical condition in a French hospital, where they are being treated for severe hypothermia. One is Iraqi and the other Somali, he told RTL radio.
It comes after more people continued to attempt the crossing. A group wearing life jackets were seen huddled together onboard a lifeboat near Dover on Thursday.
Macron has called an emergency meeting of European ministers to discuss how to stop the crossings.
He said France was going to ask for "extra help" from the British, adding that despite authorities telling migrants they were able to stay in France, they wanted to reach the UK.
The UK signed an agreement in July to pay France €62.7m (£54m) during 2021-22 to help secure the borders, but the number of people making the crossing has continued to rise.
Since the start of the year, 1,552 smugglers have been arrested in northern France and 44 smuggler networks dismantled, Mr Macron said.
Despite this, he said 47,000 attempted Channel crossings to the UK took place this year and 7,800 people were rescued.
Charles Devos, volunteer for the French National Sea Rescue organisation SNSM, was one of the first to reach the scene of Wednesday's tragedy after getting a mayday call from the coastguard.
He told French radio station Delta FM he and his crew picked up six bodies that were drifting in the water.
"We passed next to an inflatable boat that was completely deflated. What little air remained was keeping it afloat. I don't know if there were children, but we picked up [the body of] a pregnant woman and a young man who was around 18 or 20," he said.
"It's hard to say, but I was expecting this, we know it would end in tragedy, and today sadly that's the case."
Asylum claims made in the UK have risen to the highest level in nearly 20 years, with 37,562 applications in the year to September.
The Dover Strait is the busiest shipping lane in the world and has claimed many lives of people trying to cross in inflatable dinghies.
Record numbers of migrants are making the crossing from France to the UK and it is thought at least 10 other people had died in the past few weeks while attempting to cross.
This year more than 25,700 migrants have arrived in the UK by boat, more than three times the 8,469 that did so in 2020.
While the number coming across the Channel by boat has soared, that is only part of the picture regarding migrants - as this year has seen far fewer using other strategies to enter the country undetected.