For a big, once in a life time trip, you can never start too early. I've been working on my New Zealand trip for years ;-) (Hopefully 2021
)
And you don't need an excuse, just wanting to go is reason enough, travelling to foreign countries is good for the development of yourself and your children if you need another one.
1. Split stay?
Yes, if you are indeed looking at about 4-5 days at DLP and 3-4 in Paris, I would do two hotels.
As it would take about 45-60 minutes to get from DLP to Paris and vice versa. When it's the end of the day and you are tired, you probably want to go back to the hotel as soon as possible. With this plan, I personally, would split. Or stay in the DLP area as this is where you want to spend the most time.
2. Onsite:
Main benefit: You will have access to the early magic hours, which is very useful when you are travelling in high season. That being said, if you have 4-5 days, you will have time to do it 'all' even without EMH. It only depends on how many times you want to do certain rides, see a certain show.
Other benefits: Depending on the offers available, the meal plans sometimes can be a good deal. Be in walking distance of the parks (20 minutes if you stay value). Characters at the hotel. Swimming pools (at the mid/deluxe hotels).
If you would stay in one of the concierge levels, you will get a free fast pass per person per day, but with 4-5 days at the parks, that is not as necessary.
So if you would stay onsite and have budget constraints, I would definitely stay in a standard room.
However, your challenge is more in staying with 3 adults and 2 growing boys. Family rooms for more than 4 people are not widely available.
You would have to look at the Disneyland Hotel, New Port Bay and probably by that time Hotel New York will be re-opened with some options. You will have 2 double beds, and a sofabed. Or go for 2 rooms in the value hotels. Just to be more comfortable.
Instead of the Val D'Europe area, I would like to suggest the partner hotels. There are free shuttles for sure, running frequently, some have swimming pools as well. And at Campanile or Explorers you will have rooms with two double beds and a bunkbed, or a double bed, 2 singles and a bunkbed, etc.
A room for 3 adults, 2 children can also be a challenge for staying in Paris. Also here look into what will be a better option for the budget, 2 cheap rooms or 1 family room.
3. Val D'Europe Area
Yes, definitely cheaper than the Disney Hotels, but do have a good look at the offers with meal plans, as sometimes this can even out staying off site. And if your off site hotel has a free shuttle, do you have to pay for it, what are the times the shuttles go, or for the use of the subway, etc. When you have a full picture, the difference might not be that big. As mentioned, I would have a look at the partner hotels.
4. Packages.
It is possible to stay at a Disney Hotel and not have tickets for all days off your stay, incl arrival/departure day. When you do it online on the DLP website, yes, then the system will only give you that option. When you use websites like hotel.com/booking.com/expedia.com/trivago.com, you can book a room only and book your tickets online on the DLP website. Or you can of course call Disney and make a room only reservation and a buy your tickets.