If you're starting from one city's centre and heading for the other city's centre, then the train is much more convenient and probably faster overall than flying.

The downside is that the train seems usually to be significantly more expensive than flying. That, in part, reflects the convenience factor.

The best thing to do is to use all the flexible search functions that you can find. I don't think it's that easy to do on Eurostar, but at least there's only one train operator. On the airlines, BA, bmi and easyJet all have flexible search functions that allow you to home in pretty quickly on the cheaper/cheapest flights in the time period that you're thinking of.

But if it's really rather expensive however you do it, my advice would be to consider not going to Paris. A day and a half is better than the lunatic day trips that so many tourists think they should do when they've only got a few days in London anyway. But even with 1½ days you won't see much of Paris, and she is worth a long visit all by herself. If you could easily do it cheaply, it might make some sense; but if it's too expensive, don't fret and come back to Europe to see only Paris next time.