Britain has already contributed more than 60 million euros and "there will be around an extra 20 million euros", European Affairs Minister Harlem Désir told RFI.
The money will be used to boost "security of the access zone to the tunnel ... and fighting trafficking networks", he explained.
Macron earlier told the Financial Times that Brexit could scupper the Le Touquet agreement, that allows the UK to carry out border controls in France and refuse entry to unwanted migrants, echoing a warning by Cameron last month that his opponents dismissed as scaremongering.
Désir appeared to contradict the claim, pointing out that the agreement is bilateral so "there is no blackmail, no threat", but warning that Britain's EU membership facilitated cooperation through the European police force Europol and the online records of Schengen agreement states.
Recalling Cameron's offer to "roll out the red carpet" for French companies when France planned to levy a special wealth tax in 2012, Macron said he would do the same if Britain votes to leave the EU in June.
There might be "repatriations from the City of London" because financial institutions would lose "passport" rights to operate across the EU, he speculated.
Brexit was not on the agenda of Thursday's Cameron-Hollande meeting in the northern French town of Amiens, which was expected to be dominated by the migrants question.
French Interior Minister Bernard Cazeneuve recently called on the UK to "examine the cases" of those with families in the UK, especially children on their own.
There were 291 unaccompanied children living in the part of the Jungle camp that was being razed this week, according to charity Help Refugees.
The two leaders were expected to sign agreements on defence, terrorism and the construction of Britain's Hinkley Point nuclear reactor by France's EDF power company.
Britain and France are planning a 7,000-strong joint expeditionary force that should be operational after an exercise in April.
They also intend to invest two million euros in developing next-generation military drones, a British source told the Reuters news agency.
The two leaders were also expected to discuss the situations in Ukraine, Syria and Libya.
Before the summit Hollande and Cameron were to meet at the cemetery at Pozières, where some of the 400,000 British soldiers killed in the World War I Battle of the Somme are buried.