While on the phone here in my office this afternoon I glanced over at my Gitane Sprint and noticed the right side of the handlebar looked bent. I hadn't noticed this before so after the phone call I took a closer look and it, indeed, appears to have maybe fallen over at some point in the past and landed on that side?? The frame and fork look ok so I think it's just the bars. These are Atax Philippe alloy bars that say Franco Italia on them.

Is it worth trying to put a little pressure on it to see if it will straighten out or should I just say forget it and replace them?

It'll take more than a "little" pressure to fix them. Though if you've never noticed it riding it, why worry about it? Unless it's just one of those things that's just gonna bug the heck out of you and linger in the back of your mind. Then, yeah try and fix it. If that doesn't work either spring for new ones or keeping riding as is.
-Gene-

Oops - pictures, I forgot the pictures. Maybe I'm a little more aerodynamic on the drops with the right side tucked in closer to my body.

Yeah look a little bent, but it extremely difficult to bend them back and they will be weaker for it. I would recommend to continue riding them (especially if you spend most of your time on the tops) and keep a casual eye on ebay for a replacement set.