The methods of financing the purchase are varied but essentially fall into three categories:
1) payment without borrowing, from funds you already have available
2) remortgage an existing property
3) a new mortgage specific to the property
Clearly you will need to see a mortgage specialist if you are using either of the last two options. The main considerations relate to the percentage of the purchase price that you are hoing to borrow, and the currency in which you borrow the money.
There are good arguments in favour of getting a mortgage in the same currency as your main income - your monthly mortgage payments can't escalate as a a consequence of changing exchange rates. However there is also a good case for borrowing in the same currency as you are paying for the property - if large exchange rate movements mean you lose money on the value of the house, then at the same time the value of the mortgage will fall, offsetting the losses on the property.
In reality the decision will depend on your personal circumstance, but there are usually mortgage lenders happy to lend you money in either currency, and that will be able to advise you. Seek the advice of more than one lender.
Often, people buying property in France hope to rent the property out a bit, to cover the mortgage and other associated costs. This can be effective, but not always. The costs of marketing the property to attract visitors, the additional costs of utility bills, tax on the income and so on all serve to reduce the advantages of doing this. All the same, many people are already buying property in France, and using the income generated to pay for it, with the expectation that they can retire to a fully paid up property in 10-15 years, and have free holidays meanwhile.
Note however that mortgage lenders will not usually lend money for gite purchase, or where mortgage payments are dependent on receiving rental income, so you will not be able to use this in your mortgage application.
Related sections: An introduction: Buy property in France
how to choose a region to move to: Which region of france to live in
How to actually Find a property
How to finance the deal: Finances of buying in France
Completing on your purchase:Close the deal