Paris real estate is a different animal from the rest of France. Prices are double or triple those of provincial cities. Competition is fierce. And foreign buyers face unofficial but real resistance from sellers and agents who prefer French nationals.
The legal hurdles are real too. Some Paris neighborhoods have restrictions on foreign ownership, though these are rarely enforced. More practically, banks are stricter with foreign applicants. You'll need a larger down payment—often 30-40% instead of the 20% French buyers might put down. Mortgage approval takes longer. And if you're not an EU citizen, some properties are simply off-limits.