It is virtually always possible when considering buying a French property to propose an offer that is below the asking price. The crucual question is By how much?
Properties offered for sale by estate agents should have been subject to an estimation of the property's value, before being formally taken onto the agency's books with the completion of a 'sales mandate' by the vendor and the agent. The mandate sets out the agreed asking price of the property, the commission payable in the event of a sale, and the term of the mandate - usually three months renewable in the case of a simple mandate.
In discussion with his client, the agent may have gleaned an idea whether there is any room for manoeuvre in the event that a potential buyer makes a formal offer on the property. Almost invariably owner/vendors have an inflated view of the value of their property, which they may have loved and cherished over the years, and are now reluctant to part with. Emotional reactions may cloud their judgement and many do not, at this stage at least, always listen to the advice of the agent, who may have his own view of the property's saleability. (A reputable agent would not take on a property that is so over-priced as to render it unsaleable).
Buyers considering making an offer should consult their agent and listen carefully to his advice. There can be certain legitimate grounds for proposing an offer, for example if the state of the property means that extensive renovation works are required. In this case asking for a price reduction is justifiable, and you could support your request with builders' estimate to prove the point. Asking for a price reduction simply because a particular property is priced at more that you can afford leaves little ground for justifying your request. In this case, you would have to turn elsewhere and find something cheaper.
Potential sales often collapse because of intransigence by either buyer or seller, even when the two sides are only a few thousand euros apart. More often it is an unrealistically low offer by the buyer which is put forward, against the agent's better judgement, that effctively kills the sale. Well instructed agents will know or have a feel for how much leeway is possible, and may know from past experience that offers at or below a certain amount have been refused by the vendor, and simply refuse to pass them on.
Even in what is currently regarded as a buyers' market, many owners are simply withdrawing their property from the market, as many may be second homes or there is no particular urgency to sell. In every case, it is wisest to listen to you estate agent or adviser, who knows the market, knows the property and - above all - knows the vendor.