Your title is: "How to offset currency exchange losses?"
However your course of action could alternately make the following a more accurate title: "How to take on additional currency exposure / risk?"
Remember - you are thinking of the EUR being at a 'low', but that's relative to some historical period. If EUR reaches parity with the USD, then you might look back at this in 2 years and think "why did I buy EUR when it was at a high?"
If you expect future expenses in EUR [ie: you expect to retire there, or perhaps you have a summer home there and make mortgage payments in EUR], then buying EUR in advance could be one way to mitigate that risk [AKA 'hedge' it].
However if you don't expect any significant expenses in EUR in the future, then what you're really asking about is whether you should invest in a foreign currency. And the answer to that is, probably not.
Currencies are poor investments, because they do not have an inherent growth proposition. You buy stocks, because companies make things, and if those companies grow, they make more things, and you get more dividends - there is a real-world value proposition. With currencies, even if Europe's economy expands, if the US's economy expands even more, you could still lose money on your EUR investment. That's because currencies are a zero-sum game. ie: if one goes up, it is because the other went down.
Also, currencies are quite volatile, and therefore risky - there are a lot of fx investing questions on this site that give a deeper explanation into all of that. For now the key for you to understand is simply that what you are planning is fx speculation, whether you think of it that way or not.