Aiguille de la Grande Sassiere is the highest peak I know of in the Alps that (in fine summer weather once enough snow has melted from the prefious winter) can be climbed without ice axe / crampons. There's one bit 2/3 of the way up where you have to do easy rock climbing for about 6 metres, other than that it's just a (strenuous) walk.
Notwithstanding the above, the usual cautions apply: this peak is 3749m high, high enough for altitude effects to kick in and warm clothing must be carried.
The path starts at the nearest road end, obvious on any decent road map, which turns off the road up the Isere valley about 1km upstream from the barrage de Tignes, just south of a long avalanche shed.
From the road end, the path is obvious, starting up the grassy slopes to the north, there are a couple of junctions but if you take the most beaten option at the junctions you will end up climbing the peak.
The route is clear, and about halfway up you have to descend a little. After this, you ascent about 150m to the one place where it is necessary to do a little rock climbing. At the top of this there is a large cairn, make a mental note of this and the exact route for the return, as it is easy to go wrong here (I did so the 4th time I climbed this peak, and had to re-ascent 200m)