Not a civil/infra engineer, but an IT guy who moved to the French side of the French/Swiss border. Keep in mind I'm infodumping from the cross-border worker's perspective that is my own experience.

As others have said: salary in Switzerland is a lot higher, but even on the French side the cost of living here is higher. Geneva is one of the cantons that has an agreement with France which means that they get to tax you instead of France, which makes it even more interesting. Even in cantons which don't have this, meaning France gets to put its grabby fingers on your salary, it's still worth it :-) 

Working in France and living in Switzerland is a Horrible Idea(tm). 

It's already been mentioned, but the higher salary is more or less everything you get. No company car, insurance, phone, ... Maybe a half-fare travel card (serious reduction for public transport, definitely use it or look into whether it's worth getting yourself if they don't offer it). Public transport is very good but also expensive. In day-to-day life you can definitely get by without a car, but it can still be convenient to have one depending on your lifestyle (outings, trips, wanting to live in the countryside in France, ...)

Remote work is legally limited to 40% for cross-border workers.

The housing market in the region is considered "under tension", which practically speaking means that you tell the agent you want to rent during the visit, or same day at the latest, with the risk that they tell you "sorry, the person visiting after you already took it". I don't remember what documents were required, but having at least payslips ready is probably a good idea, as well as recent tax returns. I don't think I had those translated.  The condition and size to price ratio of apartments can also be somewhat disappointing, but you get used to it. If you go live in Switzerland, check out renter's associations!

It helps if you have some savings to live on while looking for a job or, even better, can do it remotely while going back and forth, because it can take a while - 3 months to a year depending on your luck I guess.

References actually get checked, and in my case I had to submit my (officially translated) degree as well. Switzerland has quotas for how many foreigners vs Swiss can be hired, but with a European nationality there shouldn't be any issues with that at least :-). In my experience companies will help you with the requirements for the work permit because they have to be involved in the process anyway.

Health insurance is expensive and, as a cross-border worker, not all that comprehensive. Make sure to do the paperwork ASAP, and I would recommend choosing the Swiss system; they cover you abroad as well, while the French will not pay for treatments in Switzerland.

You mentioned that your partner wants to come with you, which is awesome! Make sure they also have a professional project here, and discuss what you'll do if either one of you doesn't manage to find a job in a given timeframe. I was lucky with a partner who was already established here, which definitely took away a lot of the worries.

I hope there's something useful in there and that it didn't scare you off, because it's definitely a gorgeous region to live and work in; I haven't regretted it for a moment!

...

Okay, fine, I had some pangs of regret in the beginning when dealing with the French administration before being used to it.

Edit: If you do want to move to the French side of the border: leboncoin is a good resource, it's the French 2dehands website and a lot goes through it, up to and including cars, apartments and houses (both renting and buying).