The company is due to begin recycling work on the 255-metre Clemenceau after Easter, in a 10m euro (£8.75m) project which will create an additional 200 jobs.
The vessel contains 700 tonnes of asbestos-contaminated materials and was recalled to France from India in 2006 amid concerns over its toxic elements.
Jean Kennedy, leader of the Friends of Hartlepool, a local community group which led the fight over the issue, said: "Here was a ship laden with the worst possible toxins and they want to bring it to this country to get rid of it.
"We've now got a ticking, toxic time bomb and we're going to live in a nightmare haze of toxicity for the rest of our lives. We live in a town where we're breathing it every day of our lives."
Peter Stephenson, the chairman of Able UK, dismissed the objections of Ms Kennedy and others.
He told the BBC: "The protestors had all the opportunities over the last five years. There was a public inquiry. It's been looked at by all the proper authorities. It's been all sanctioned.
"What we're going to do is what we were going to do in the first place - same methods we've used for years. So I don't see any problem with that."
He said it would take up to two weeks to investigate what work is required, then five months of "remediation works" before the actual dismantling begins in the summer.
We have taken into account the concerns of people and factored into the permits regulatory controls to allay those concerns
The Environment Agency's Bob Pailor
The Environment Agency says it will ensure the ship is recycled in a safe and environmentally sound manner.
The agency's Bob Pailor said: "The operation will be regulated heavily by ourselves, the Health and Safety Executive and the borough council - and provided the regulations are adhered to no harm will occur.
"We have taken into account the concerns of people and factored into the permits regulatory controls to allay those concerns."
The Clemenceau, once the pride of the French navy, has spent the past few years being moved around as officials tried to find a final resting place for the vessel.
Launched in 1957, it sailed more than a million nautical miles and saw service in Lebanon, the first Gulf War and the Balkans before being decommissioned in 1997.
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