We've just come back from a two and a bit week trip to France. We were originally intending to do the French Divide ITT but we both scratched at about a quarter of the distance, we then spent a week touring around Brittany.
We both had rigid MTBs, I used a Cotic Solaris, my wife a Stooge. These were fine for the FD but a bit much for the touring side of things. The FD was quite a bit of easy stuff, road and canal paths and the like, but then there'd be a kilometre steep descent where it was borderline needing a FS bike. The touring was a mixture of quiet roads and "voies vertes" which translates as "green lanes" but they are nothing like the UK idea of green lanes, it's better to think of green as in "Eco". They are quiet roads, canal tow paths, shared footpaths, old railway lines and are designed to be family friendly. Some of them are very long, we did part of one that went between Roscoff in Brittany to Kiev in the Ukraine!
Most of the time on the Voies Vertes you'd be fine on a road bike but there's the odd section of gravel farm track which wouldn't be nice. I'd go with the Giant even if you don't end up using any of the VVs.
As for kit, we were travelling very light as we were set up for the FD and our tarps and bivy bags caused some curious looks on the campsites when we were touring: "Look like sardines!" was one comment
Some people we saw touring had masses of kit - Bob trailers or similar were quite common - but you are never far away from shops and restocking. Most towns and even some of the villages have a "camping municipale" with costs ranging from 7 - 22 Euros per night. If we were to go touring again we'd use a lightweight two man tent like the MSR Hubba Hubba, it wouldn't add much to the weight of camping kit over the tarp/bivy combo especially when split between two. Of course the problem is that quality lightweight (and non-bulky) kit costs money.
Here's what my bike setup looked like.
Adding a tent (or my half of one) would just make the bag on the handlebars a bit bigger. The biggest/bulkiest thing to be added would be a stove and assorted paraphenalia, sort of depends what you want to cook really. We'd be happy with an coke-can alcohol stove to make brews and eat out but that's not cheap! You don't need much kit really, France at that time of year is pretty warm, most nights I was sleeping on top of my bag not in it.