You pay a small amount every month so that you are sure to get enough money to pay for your funeral as some point in the future. Funeral insurance.
[ I work for a French insurance company and am describing the standard features of a French funeral insurance product. Local variations may very well exist. Consider the following as a "thought-starter" and not a definitive answer. ]
Say you are 70-yrs old, decent health, decent retirement income, some savings, couple of children (now grown-up) and a few grand-children.
You may want to anticipate how things will go when you die.
As you die, all your assets are frozen, so that a proper inheritance inventory can be made, your estate shared among your descendants / other beneficiaries if you have left a will, etc.
As a result, in the vast majority of cases, your children will have to pay for your funeral before they can recoup the cost from your savings
The average funeral costs about €3 000 in France (excl. the slot at the cemetery). Range from about €1 500 to over €6 000 
This is not a awful lot of money, but it is not a small amount either and no-one wants to have to deal with finding cash when also grieving the loss of a father / mother and doing all the other paperwork
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And you do not know when you'll die -- so it is even harder to anticipate how your family will act when the time comes.
So you can take an insurance contract where:
You pay, say, €40 per month for a set €3 000 cover
You tell your family about the insurance contract, including giving them the policy number and the contact details (!!)
If you die in the first 2 years, you get nothing in return (*)
When you die, at any point in the future, your family calls the insurance company, faxes a proof of identity and a copy of the death certificate, and the €3 000 can be transferred either
To a designated family member who will use the cash to pay for the funeral expenses, OR
Directly to the funeral company, again to pay for the expenses
On occasion, the funeral company can send the invoice (up to the €3 000 directly to the insurance co.)
Any cash difference between the €3 000 cover and actual expenses to be paid by / reimbursed to the family / beneficiary
It should be noted that the laws (in France) are evolving to make sure the money is indeed used to pay for funeral services. There were some abuses with people receiving €5 000 from the insurance and then only spending €1 000 on the funeral. Pretty odious behavior is you ask me to basically embezzle Granny's money -- not to mention that the tax authorities did not like that.
It can happen that you live up to 110: you would have paid €40 a month for 40 years (almost €10 000), just to get €3 000 when you die.
Well, very few people do live up to 110. Many die at 75, only 5 years after the beginning of the contract. Those people paid about €2 500 and got €3 000.
Your long life compensate the short life of others.
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And the insurance company has salaries to pay too...
(*) That is to avoid people with critical illness take on the insurance just before they die. Insurance is about getting protection from random events -- if you know you'll die in 2 months, that's not random. (Sad, but not random).