Those elevation profiles look like they're from Google, which tends to underestimate. The second would end up being rather hilly. That would be a good workout on a singlespeed, unless it's frustratingly low-geared for the first. Plenty of people would do it; I might, but wouldn't recommend it for someone not currently riding.
For a commute like that, I'd look for a second-hand hybrid* with gears - you should get fairly recent 3x7 or 3x8 gearing, with enough room in your budget for a good lock, lights, and helmet. This would also handle any rough surfaces short of actual mountain bike trails, with reasonable tyres.
I suggest you aim for being able to add a pannier rack later.
Looking new on Decathlon, you could still get something reasonable - around €200 you get 1x6 gearing - old fashioned but Shimano so you could get spares. By around €300 it's 1x9 gearing, own brand and Microshift, but spare parts for repairs shouldn't be problematic. Note that some very cheap supermarket bikes / bicycle-shaped objects (BSOs) have compatibility issues when parts wear out, and are best avoided. The upgrade from V brakes to mechanical discs, and the other higher specifications you get for the higher price don't really matter, though you save nearly 1kg. Pannier rack compatibility looks almost universal in this category on Decathlon.
* The most common usage of Hybrid seems to be equivalent to vélo tout chemin or VTC; the examples I can see on Decathlon are the more rugged ("trekking") style of hybrid, while the light (sometimes called "fitness") hybrids are treated as flat bar road bikes. They'd also be fine on all the French roads I've ridden.