The current fall of the Euro vis-a-vis the US dollar was prompted more by the ECB's expected quantitative easing (i.e. printing money) to try to stave off deflation than anything else. Though stronger relative expectations for growth in the US vs the Eurozone is another factor in the movement of exchange rates.

A stronger dollar affects airfare more indirectly, in that strong dollar over a longer horizon generally leads to lower commodity prices, such as oil (priced in dollars).

However, the days of $300 TATL airfare are likely long gone; they were the product of the pre-joint venture era when there was little capacity coordination or control on most TATL routes. Today the major alliances coordinate capacity and schedules much better in order to match supply of seats with demand in order to maximize revenue.

Selfishly, a weaker Euro is appreciated for my upcoming trips to France and Italy; I had baked in a $1.40 Euro in my planning, so given the peanuts I usually spend, I might be able to splurge for a nice dinner at the end and still meet my budget.