I agree with Richard - there are possibilities for a 'running approach' to Alpine peaks, but you have to pick the right area. I visit the Maritime Alps above Nice every year for short multi-day peak-bagging tours before my kids arrive for a normal family on the coast. Eminently suitable to tackle fell-running style, which is what I do - wear innov-8s, carry OMM sac etc. Generally non-technical peaks, around 3000m, usually mildish scrambles with tricky route-finding and awkward terrain (not always runnable!). Some big snow patches, which make kahtoolas or similar advisable, although you can get away without them esp late season. Normally get the peaks to myself (locals do them on skis in spring).