What is a 'cheap' property?
Does 'cheap' merely mean 'affordable without a mortgage' or something more complicated ... when talking about French property prices?
The rule of thumb when buying French property is that if it's under €100k then it's cheap and probably buyable without having to beg for a mortgage. But there are exceptions to this rule and it's worth taking the time to think about this and find the properties involved.
A property selling for under €100k is either a wooden chalet, a village house (without garden) or a ruin. The chalet is fine: move in and enjoy! The village house might well be in good nick but will inevitably need re-wiring, re-decorating, double-glazing and a thorough look at the plumbing. Bathrooms nearly always have to be ripped out and updated. In other words, there is always a minimum amount of structural work to be done, incurring costs.
Assuming you buy for 100,000 plus the notaire's fees (say 8,000) and you put in 40,000 or so in wiring, glazing and plumbing, you are now about €150k out of pocket. If you wanted to actually live in the house full time then this is not a bad bargain. But if your plan was to let the place out as a gîte over most of the summer and use it in the low season for yourself then you might have been better off buying something more expensive and more substantial in the first place.
Consider this: you buy a village house which is already fitted out as two gîtes. Depending on the location this could cost anywhere from 120,000 to 200,000. As soon as the ink is dry on the contract you let out one of the gîtes for, say, 500 a week. Over the next 12 weeks this gite will bring in around 6000 (whereas in the first example this is the period during which you'll be renovating the place and arguing with friendly artisans). The more the purchase price the higher the weekly rental, in general. In other words, you could have taken out a loan for the amount needed in excess of 100,000 and paid it back within a 7 year period using the revenue from one of the gîtes. And had the other one to use as a pied-à-terre.
The same logic can be applied to more expensive property: buy a 'ruin' (usually a maison de maître or ancienne couvent) and you'll be throwing bucketfuls of money at it for years without seeing any progress, but invest in a solid 'going-concern' for quadruple the amount and you get an instant return on investment. Buy at €400k and you'd expect to let out the gites on site for around 35-40k pa. Buy for €800k and you'd expect anywhere from 60-80k in rental. In other words a ROI of 8-10%.
Bank managers love these sort of figures ... and they control the mortgages.