These are the best hours to trade the Euro

The USD is the top-rated currency in terms of Global Liquidity. The Euro is considered the second. After that, is the Japanese Yen and the British pound. Because of the strength of these currencies, most Forex Traders, trade pairs consisting of currency from this list. The Euro can be traded from Sunday evening to Friday afternoon in the United States.
Since the USD/EUR pair is the most liquid currency pair on the market, it is also the most popular and many Forex traders concentrate only on trading that currency pair. This pair usually maintains a tight spread during a 24-hour period and traders will see tradeable trends always of day. This pair often lends itself well to trading channels and swing trading which is another reason it is so commonly traded.
Clearly, there are periods during the trading week that have higher volumes of trades and time periods of lower volume. During the periods of time where Forex Traders are more active, the spread is much smaller than during the quiet hours. A common mistake made by inexperienced traders is to take advantage of the fact that Forex can be traded 24 hours a day. Just because you can trade at all hours of the day, does not mean that you should.
Forex pairs that include the Euro are very often subject to world events. Though natural disasters and other world events are difficult to predict. The part that is predictable is economic news and when it will be reported. Eurozone monthly economic reports are released at approximately 2AM EST in the US. This news will spark increases in trading for EUR pairs up to an hour before and up to 3 hours after they are released. United States economic news is usually reported between 8:30 and 10 AM EST, which again will cause a spike in trading of the popular pairs that include the Euro and the USD.
Considering that the USD/EUR is the most popular pair it makes sense that it is most commonly traded in the hours that both the London market and the NY market are open. That will of course differ depending on what time zone you are in when you are looking at this information. The three-hour window that both of those markets are open is between 1PM and 4PM GMT. You will see the most movement in this pair between those hours and the most opportunity for profit.
In short, time your trading of Euro based pairs on either the economic reporting time table or the overlapping market times. It is not always possible to be this specific, so be aware that the general window for trading Euro is between 7AM and 8PM GMT and make sure to follow economic reporting so that you know what to expect.