This is what mine looks like:
Just one sad little flower.I read your supposed to prune in the winter, but that has passed. This one is kept indoors becasue it's still chilly outside.
The number of blooms increases as healthy plants mature. If you plan to keep the plant in a container, it would prefer that the container was outside in full sun whenever temperatures allow (above freezing). The size/age of the plant and how much energy it has to devote to reproduction (blooms) ultimately determines bloom profusion. Since any energy the plant makes comes from sunshine, you should be giving your plant LOTS of it - and not through a window.
Also, root maintenance, if the plant is to be left in the pot, is essential. You should let the plant go dormant over winter, lift it from the pot in spring, bare root/root prune it, and put it back in a/the pot to continue growing. If you don't maintain the roots, you can count on a plant limited in growth/vitality/bloom numbers.
The plant doesn't tolerate wet feet, so count on using a very fast draining soil. The gritty mix would be perfect for this plant, and would make repotting chores easy. A 3:1:2 ratio fertilizer (examples: 24-8-16, 12-4-8, 9-3-6) used regularly is a very good choice.
I second Al's comments. I've given up on French Lavender and have had good success growing the English types in my gardens. I'll try to post photos as my younger plants come into bloom. I grew them from seed.
Lavenders are more Mediterranean in origin, I believe... so they do like a more dry, free draining soil. Wet feet will definitely not do them any favors. Also, when grown indoors, keep a close eye out for spider mites.
I would love to grow the French type... but it's simply too much work for me when combined with what I already have on my plate... so I've given in to the idea that if I want nice lavenders, I'll stick to the ones that are hardy to my zone, and I'll also grow Russian sage and other purple perennials to help echo that lovely color.