Four members of a Kurdish-Iranian family died when their migrant boat sank on Tuesday.
They have been named as Rasoul Iran-Nejad, 35, Shiva Mohammad Panahi, 35, Anita, nine, and Armin, six.
Their 15-month-old son, named as Artin, is believed to be still missing.
They had set off for the UK in a boat carrying as many as 28 people – 10 more than it was designed to carry, the PA news agency understands.
Search and rescue boats and military resources desperately scoured the sea off the French coast for hours on Tuesday looking for any survivors.
But nightfall brought a halt to the rescue operation and searches did not resume on Wednesday.
The family were from a village near the Iranian Kurdish city of Sardasht, West Azerbaijan province, northwest of Iran.
However they left the country due to economic hardship.
They passed the Iranian border into Turkey earlier last summer, then proceeded to Greece, Italy, and France.
The family are believed to have attempted to move from France to the UK on a train twice but both attempts failed.
They then decided to reach the UK by sea, PA understands – a journey that ended in tragedy.
“The way to honour their memory is to ensure that no other family in their circumstances feels forced to make the same crossing.”
French authorities had said that the children who died were aged five and eight.
More than 7,400 migrants have arrived in the UK after making the crossing so far this year, according to PA analysis.
Home Secretary Priti Patel – who said she was “saddened” to learn of the deaths – previously pledged to make the route across the Channel “unviable”.
Immigration minister Chris Philp promised a “new, comprehensive action plan” to stem the latest surge of crossings when he met French officials two months ago alongside the newly appointed clandestine channel threat commander Dan O’Mahoney.
At the time, Mr Philp said everyone was working “at pace” to tackle the problem and insisted both countries were committed to the cause.
Meanwhile, military planes started to survey the Channel for emerging crossing attempts after the Home Office asked the Ministry of Defence for help.
But critics branded this a political move in a bid to show action, claiming the measure would not change anything.
The efforts followed repeated previous meetings between French and British ministers and officials on the subject in recent years.
In November, the Foreign Affairs Committee warned the Government its own policies meant migrants were resorting to more dangerous routes and the number of crossings would rise.
Ms Patel was a member of the committee at the time of its inquiry, which recommended expanding the legal routes available to asylum seekers.