Re. First mistake - openly stating what your budget is.
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Good point, except that this is a Forum, not a real estate agency! Here it is possible to be forthright I think.

A couple of years ago I walked into an Agency in the Poitou and asked them what they had on their books and the man asked what my budget was. I refused to answer and he then refused to carry the matter any further. Two minutes later I walked out. Fortunately not all agents in France are so obtuse.

Second bit of advice, related to that above: Don't be bullied!