David Cameron and Nicolas Sarkozy are to sign the treaties during their London meeting.
One centre will be set up in the UK to develop nuclear testing technology and another in France to carry it out.
President Nicolas Sarkozy was greeted by David Cameron as he arrived for the summit, which will also outline plans for a joint army expeditionary force
No 10 called the measures "practical", but Labour said they left "big questions" about the UK's defences.
A Downing Street spokesman said: "This summit marks a deepening of the UK-France bilateral relationship. Ours is now a strategic partnership tackling together the biggest challenges facing our two countries."
A ceremonial Guard of Honour lined the steps at Lancaster House, in central London, as President Sarkozy arrived on Tuesday morning.
The summit comes two weeks after the UK government announced cuts to its armed forces, in the first strategic defence review since 1998, as part of savings aimed at reducing the country's budget deficit.
Under the plans £750m will be saved over four years on the Trident nuclear missile system by cutting the number of warheads.
Harrier jump jets, the Navy's flagship HMS Ark Royal and planned Nimrod spy planes will also be axed, but two new aircraft carriers were spared.
This package has been agreed because both countries still want a military role in the world but cannot afford to do so much on their own anymore.
The "joint expeditionary force" will be deployed by a joint political decision and will come under a single commander to be chosen from either country at the time of the operation.
The carrier-sharing plan does not mean that each side will simply use the other's carrier at will.
The one who owns the carrier will have to agree on its use.
The testing of nuclear warheads by technical means is a way of ensuring their effectiveness without having to test-explode them, but each side will still control their own warheads.
The nuclear treaty will establish a centre in the UK to develop testing technology and another one in France to carry out the testing. Warheads will be tested by technical means to ensure their safety and effectiveness, without having to test them by explosion.
It is understood that each country will still control its own warheads, and that nuclear secrets will not be shared.
Asked why Britain and France did not jointly buy nuclear weapons to replace Trident, Defence Secretary Liam Fox told BBC Radio 4's Today programme the UK wanted the "most appropriate" nuclear deterrent and had a "particularly close" relationship with the US on Trident.
"We're not thinking of buying new missiles - we have the Trident D5 missile. We don't have to think about new warheads until 2019.
"We do however have to maintain the safety of the warheads we have at the present time... therefore it makes sense that we become involved in the facilities for the experimental physics that will allow that to happen.
"That's a big cost saving to our taxpayers on both sides of the Channel but it does give us the ability to maintain separate nuclear deterrent programmes."
The other treaty will allow the setting up of a "combined joint expeditionary force", thought to involve a brigade of about 5,000 soldiers from each side.
Each country will retain a veto for each operation, which will operate under one military commander to be chosen at the time.
The UK and France have also agreed to keep at least one aircraft carrier at sea between them at any one time.
Each will be able to use the other's carrier in some form, certainly for training and possibly operations.
Meanwhile, France is to use British A400M fuelling aircraft when there is spare capacity, with plans in place for common maintenance and training.
Joint work on drones, mine counter-measures and satellite communications is also proposed.
Dr Fox told the BBC there had been a "great deal of hysteria" in the media about the idea of British troops coming under French command.
"Under the existing Nato system our troops could come under Turkish or Polish command. There's nothing new about that.
"This does not affect our special relationship with the United States. It gives us economies of scale and helps us to welcome France back fully into Nato."
Asked who would decide what happen if the French were involved in operations about which Britain was not enthusiastic - at a time they were sharing Britain's aircraft carrier - he said: "That would depend on what the other nation thought. This is not a question of our military assets coming under the control of any other power than the United Kingdom."
Liam Fox: "It is a very important step to improve cooperation with France."
He said it made sense that training could still be carried out while a UK aircraft carrier was in for maintenance - "if we are able to have agreements on the military operation that is fine, but we have to maintain our sovereign independence wherever the United Kingdom's interests require it".
In a statement, the French presidency said the nuclear test centre in Valduc, eastern France, would start operations in 2014.
The Valduc laboratory would work with a French-British research centre based in Aldermaston, Berkshire, it added.
Together the facilities would involve "several dozen" French and British experts and cost both countries several million euros.
It said scientists from both countries would be able to ensure the "viability, safety and security in the long term of our nuclear arsenals".
The UK's shadow defence secretary Jim Murphy said: "I support the government's emphasis on international co-operation, taking forward the good work of the last government.
"We share common threats with countries such as France, from terrorism to privacy to cyber-attack. Deepening military ties is an essential part of modern defence policy.
"Interdependence, however, is different from dependence, and binding legal treaties pose some big questions for the government."
Mr Murphy also questioned whether the the UK was entering "an era where we are reliant on our allies to fill in the gaps in the government's defence policy".