The base of the Eiffel Tower (seen here from the Place du Trocodero) encompasses a wide area, with ticket booths at several corners. Check around and see which one has the shortest line-ups.
Lots of people will be milling around beneath the Tower, and some will be trying hard to sell you souvenirs. f you're not interested, don't give the slightest encouragement: even a smiling "I don't think so" is an invitation for more dialogue.
On the other hand, you might wish to buy. Generally prices will be highly inflated, but will drop quickly with bargaining. We bought souvenirs in the Tower giftshop, and later were offered similar items by vendors at half the price. We adults may turn up our noses at tourist trinkets, but many kids really treasure their little souvenirs.