Do you know http://www.fietsrouteplanner.eu/ ? That should be your first stop for planning the route.
Without looking at above planner I would not avoid the Alps. It won't be easy, but it is not impossible. France south of Paris is geneally not an easy terrain for a cyclist, thus I would not cycle 1300 kms more through hilly and mountainious terrain just to avoid the Alps. My suggestion would be to follow the Rhine and then look at crossing the Alps at one of those two points:
1) The Via Claudia Augusta is the easiest way to cross the Alps. The route goes from Augsburg in Germany to Venice in Italy, crossing the Fernpass and the Reschenpass. For the hardest parts there is a special shuttle service by the Austrian Postbus.
2) Switzerland can be done on a bike. Basel to Geneve is actually very easy to do because it is mostly flat. The problem in your case is getting from Switzerland to Italy. Take a look at http://www.veloland.ch/ for more information. The site suggests the National route number 3, from Basel to Chiasso.
You can find the profile here:
As you can see you only need to get across the Gotthard - and you can take the train from Erstfeld or Wassen to Airolo (price 15 CHF) if you find that it is too hard.
Some more tips:
If you are a complete couchpotato you can expect to cover 30 kms per day, going up to 60 kms per day after 3-4 weeks of cycling.
If you live in the Netherlands and were born on a bicycle or cycle 15 kms to work every day covering 50-70 kms per day will be realistic in the beginning, pushing towards 120 kms after a few weeks. This is on flat terrain. Mountains will be different, but it only gets hilly towards the end of the trip. At this point you should have enough stamina to deal with them. The good thing about big mountains is that while it takes very long to get up the ride down is great - down you easily cover 30+ kms without any effort at all.
Tuscany will be the hardest part of your trip. All those people who tell you how nice it is to cycle in Tuscany have probably never done it. The hills are steep, the angles change frequently and the mix of climbing and going down is far more taxing than going up one big mountain at a steady pace.
You need good equipment. A racing bike or trekking bike with 3x9 (27) and hydraulic brakes or disk brakes bought at specialised shop is essential. An "omafiets" is not suitable. You can find a list of brands that is popular with long-distance cyclists here: http://radreise-wiki.de/Fahrradhersteller
You should also have good waterproof panniers. Many Dutch long-distance cyclists use the Ortlieb panniers offered by Globetrotter (www.globetrotter.de) - brilliant orange, discounted price and very good quality.