Small boat migrant crossings are becoming "a major threat" to the UK, MPs have been told.
The Home Affairs Select Committee was hearing evidence after Brexit Party leader Nigel Farage claimed French ships were "escorting" migrant boats.
The Home Office said migrants had been "shadowed" in case their vessel sank.
Ex-Border Force chief Tony Smith told MPs migrants knew UK boats would pick them up, adding: "This is becoming a major threat to the UK border."
Mr Farage had taken a boat and camera crew into the Channel to film crossings on Wednesday.
Ruth Edwards, Rushcliffe's Conservative MP, asked Mr Smith about the footage which she said appeared to show "a French naval vessel accompanying a migrant dinghy with migrants in it from French waters into British waters".
Mr Smith said: "International law is that health and safety must come first and any vessel that sees another vessel that's in that state, with women and children on board, with no navigation equipment, at risk of drowning, should immediately take measures to take them on board.
"[Migrants] have seen that if you can get close to a British vessel, then essentially you are guaranteed to be taken into one of our ports and you are pretty well guaranteed - these are vulnerable people - to be taken into the UK system."
He also told the committee: "This is all driven by money and smugglers. They will be showing people pictures now of what they were seeing on Sky News yesterday - 'this is all you need to do, pay us the money, we'll put you in a dinghy and push you off'."
Mr Farage posted on his Twitter account claims that he "witnessed the French Navy escorting illegal migrants into British waters".
After he released video on Wednesday, a Home Office spokesman said Border Force intercepted five boats that day, adding: "The one 'spotted' by Mr Farage was already on our radar when he called it in."
The Home Office said both Home Secretary Priti Patel and the French interior minister were committed to stopping Channel crossings.
The government also claimed the French Navy had been following international law, saying: "It would be illegal to intervene with the boat. Instead, the navy is committed by law to save lives at sea, and consequently shadows boats that are at risk."
Further attempted crossings were reported on Friday after Border Force dealt with a boat carrying 13 people in the early hours and French authorities also dealt with two incidents.
Dover's Conservative MP, Natalie Elphicke, said a tougher line was needed, adding: "I understand this is due to safety. The safest thing would be to stop boats leaving and return everyone to France."
Earlier this month, Mr Farage complained to Kent Police because officers had visited his home after he had gone to Dover to report on migrant arrivals.
He said the officers had told him they wanted to remind him about temporary travel restrictions in place as a result of the coronavirus pandemic.
Kent Police said it would be inappropriate to comment.