As someone, who has two kids who are completely fluent in French, it is very possible to achieve this. My husband and I only speak English at home and we don't know to speak more then a few basic words/phrases in French.
I started out getting a French nanny 6-8 hours a week for my daughter at the age of 4. I also sent her to 3 after school French clubs that I found in the area (Monday, Thursday and Friday weekly). The French nanny we had during the weekend and then I would also try to practice with her and teach basic words in phrases (while I learned them as well!). The game changer was when my daughter got accepted into a French bilingual school near by. But when she joined mid year, she already knew at least 200 words/phrases in French. It takes a lot of effort, but she is fluent now after just over a year in the school. We also got a French au pair recently and my children do not realise she can understand English, this is what forced my children to speak French and they have not spoken one word of English to the au pair form day one. My son has been at the school less then a year and he is also fluent. The au pair is with them 25 hours a week and she lives with us. She only speaks to them in French and pretends she does not understand English (sometimes I slip and speak to her in English). My kids remind me she does not understand English and they translate to French for me.
I know kids that go to the German school. They have a German dad and American mom. I think as long as you teach your son basic German, get the German speaking nanny or even better a live in German au pair (that does not speak to them in English) they will be able to learn enough to get by and start at the German school. Is it possible to get a German live in au pair? You can find one via aupairworld.com. If not, you could get a German nanny, but for children to speak the language, they need to feel a need so she would need to speak only in German and pretend not to know English. And you would need to teach your children basic phrases at first, so they could communicate the basics with the nanny. For example - toilet, I'm thirsty, I'm hungry, I'm tired, i want to play, colours, fruits and veggies or different foods they like etc. You can also find youtube German cartoons. Peppa pig is REALLY good for this. The easy and repetitive language helps the kids learn. My sisters daughter is speaking German and watches the peppa only in German (but her husband also is German and speaks German to her daughter, but peppa helps). I would also play German kids music and audio books during bath time or breakfast etc. If you can read German, I would start buy some easy basic German books (maybe more peppa?) and then read them one book a night in German. You could start out with 7 books and just re read them. When you re read the books, the kids learn the words. I bought loads of French kids books on amazon.co.uk. I am sure you can find German. Actually, I also bought a great Usborn German words sounds book for my sister. I also did this in French for my kids and they loved this. It teaches the correct pronunciation for the words and kids can even look at it by themselves. Best scenario would be if you can get 25 hours a week exposure from native speaker. But if you can only get 10 hours a week, you would have to supplement with lets save 5 hours a week of tv exposure, 5 hours of music/audio book exposure and, 5 hours of reading books at night exposure. Your aim is to reach 25 hours a week of exposure. Once they start school it would be a lot easier if they get into the German school.
It is possible to find your own nanny by doing research and checking websites like care.com. I checked out littleoneslondon before and they charge quite a lot of money to do the search for you.
Where there is a will, there is a way. It is not easy, but the more effort you put, the more likely your children will be fluent. I see some children who are not fluent after a couple years in the bilingual school, but that is because their parents do not put effort in outside the school.
Any questions, please ask.
Good luck!