I am a bit of a Tour de France fan and so wanted to have cycled all the famous cols to experience it for myself. Not wanting to take years over it I looked into doing all the Alpine cols in as few days as possible. What I found out was that there route called La Route des Grandes Alpes which is promoted by the french tourist board: http://www.grande-traversee-alpes.com/je-voyage/par-la-route/la-route-des-grandes-alpes.html
It is recommended as an 8 day route and misses a couple of TdF classics like the Col de Joux Plane where Lance Armstrong was in all sorts of trouble in 2000. There is a complication in that the climbs of Alpe d'Huez and Col de la Croix de Fer are stuck out on a loop in the West so I decided to save those for another time. The standard route also missed the Col de la Bonette which was on the 2008 tour and as the highest road in Europe really had to be done.

It was brilliant, I loved it. It is so do-able. I had the luxury of Tess her mum and baby Alice as support crew for the cycling team of me and my friend Clive. However, with 4 cyclists and a rental Citroen Picasso (pick-up from Geneva airport and drop off at Nice) it would be easy for all to enjoy cycling up all the cols (each team member takes turns to set out by car, park at the top of the next col then cycle back to join the others and cycle back up the col with them).
Cycling from North to South turned out to be a great decision since you do not get too hot on the way up and you get warm sunshine on the South facing descents.
It would be difficult to do the route much later than we did at the start of September since the weather gets a bit cold and risky and the season for the hotels comes to a end. The earliest it could be done would be around the start of June though there is always the risk of a snow storm closing any of the high cols.
The thing I really love about cycling in France is the contrast of the attitude or car drivers and pedestrians towards you. In the UK I might expect a few shouts of something along the lines of "get off the f#*cking road you lycra fa*#ot". In France every day you get a few shouts of "Bon Courage!" and "Bravo!".
5 days - 660km - 15 big cols - 15,000m+ of ascending
Col de Joux Plane 1691m (10.9km avg. 6.5%)
Col de la Colombière 1613m (16.3km avg. 6.8%)
Col de l'Aravis (11km avg. 5%)
Col des Saisies 1657m (15km avg. 6.4%)
Cormet de Roselend 1967m (20km avg. 6%)
Val d'Isere 1850m (15km avg. 5.8%)
Col de l'Iseran 2770m (15km avg. 5.9%)
Col du Télégraphe 1566m (11.8km avg. 7.3%)
Col du Galibier 2646m (18.1km avg. 6.9%)
Col de l'Izoard 2361m (20km avg. 5.7%)
Col de Vars 2111m (19.4km avg. 5.7%)
Col de la Bonette 2802m (24km avg. 6.6%)
Col Saint-Martin 1500m (16.5km avg. 6.2%)
Col de Turini 1607m (15.3km avg. 7.2%)
Col de Castillon 707m (7km avg. 5.1%)
You can view my information about the route and accommodation here:docs.google.com/View?docid=ddg9mgw6_17g28ppqd8
Detailed info on the climbs can be found here: www.climbbybike.com