Were there any democracies in Europe that pre-date the French Revolution?
Pericles’ Athens.
A possible and rather little-known candidate is the Rzeczpospolita, usually called the Polish-Lithuanian Commonwealth in English. It wasn’t a full democracy, since only a small percentage (about 10%, the szlachta or nobles) were enfranchised. But Athens didn’t give the right to vote to everyone, and few democracies gave full enfranchisement (i.e. women’s suffrage and universal male suffrage) until the 20th century. It had something of a constitution, and a senate and parliament. It was at least as democratic as England around the same time; indeed, England, and later Great Britain/the UK, is probably a good candidate too. But the Rzeczpospolita seems to have been more designed around the idea of a republic than the British constitutional monarchy.
A number of the regions which now make up Italy were democracies / republics at various times during the middle ages - Siena, Florence, Pisa etc.
As Roches has already pointed out, citizenship and enfranchisement were (and are today) subject to conditions.
Iceland (culturally European at least).
Define “democracy.”
If an elected Parliament with power is the criterion, then Great Britain qualified as of 1688.
But, as I suggested before, if the criterion is that every adult citizen has the right to vote for their government regardless of race or gender, the United States, Canada, the United Kingdom, and France were not democracies in 1915. (At least, in the case of the US, on a federal level, as some states had women’s suffrage by that point.) Many countries which were relative democracies did not have universal male suffrage in the 19th century either – they denied the right to vote to slaves, those who did not own land (i.e. much of the working class), those who did not have sufficient assets, Jews, etc. On the other hand, at the same time as this, some countries had absolutely no popular representation whatsoever, or had only a ceremonial ‘election’ (as with the Holy Roman Emperor; for a long period of time, a group of princes consistently ‘elected’ the head of the house of Habsburg to the office). There have even been (and still are) countries that were technically democratic, in they had constitutions and elections in which everyone could participate, but where there was only one choice on the ballot.
San Marino, a “postage stamp” country located completely inside Italy, is often described as “The world’s smallest and oldest republic.” I’ll leave it to someone more familiar with the place to say how democratic they are (Technically, there are no pure democracies in the world).
And if the criterion is that every citizen who can be treated as an adult when he breaks the law has the right to vote for his government, the United States still isn’t a democracy today. 
There was a Dutch Republic kicking around for quite a while, at least in name.
Don’t confuse a republic with a democracy, because not all republics are democratic. Rennaisance Venice was a republic, with an elected Duke, but the Doge of Venice was only elected by a few rich nobles, and wasn’t democratic in any sense of the word. The same is true with a lot of the earlier republics mentioned in this thread.
There were of course a wide spectrum of political systems in medieval Europe - Florence is probably a good example of a system approaching democracy, depending on your definitions.
Elections were held regularly, power was distributed over a number of individuals and councils. For long periods nobles were actually excluded from holding office. At other times powerful families were able to exert exeptional influence through their wealth and through manipulation of the political process via the guilds.
In 2005 this still leaves the problem of access to citizenship, if we consider that citizenship is a necessary condition in acquiring the right to vote.
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For many years, “Republic” did not mean anything other than “not a Kingdom”. I don’t think the USSR (Union of Socialist Sovietic Republics) was much of a democracy, you know.
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Some countries that never would have thought of calling themselves “democracies” had a (partially) elected Parliament. The idea of medieval monarchy that many people have, where the king does whatever he fancies, is actually based on XVII century politics - or at least on what Louis XIV would have liked (he still had to give in occasionally). Many medieval monarchs had to deal with Parliaments where part of the seats were hereditary and part were elected. In many texts you will see a mention to “seats belonging to the Church”, but they were hereditary too… it’s only that abbots don’t inherit from Dad
As to the issue is it really a Democracy if girls can’t vote here is a List of Universal Sufferage in selected contries