I'm certainly no dance instructor, but I've put in more than enough years as a dance mom to weigh in.
It's not a big deal for the teacher to be using the french terms, even w/ 3 year olds. As several others have pointed out, it's not french to the kids, it's just a name.
3 year olds absolutely do learn some technique when the class they are in is a ballet class. Yes, other classes may be called creative movement, mommy & me, whathaveyou. You can even learn snips of ballet movement in these types of classes, but it is a bit less likely. Now, stating it as if 3 year olds are "learning technique" is both true & a bit misleading. Generally if you listen to young children's ballet lessons, you'll likely hear something like "point your toes, let's put our toes out & point them like this, kind of like a key going in a keyhole". It's guaranteed that even the most precious little ballerina giving it her all is not going to achieve proper foot position at three. A skilled instructor will know when a dancer has hit her best attempt of the technique in question by a dancer of that age, compliment & encourage the dancer to maintain that as her benchmark at that age. With every year/increase in development the instructor will refine the dancer's technique until they are of an age/developmental maturity to master that particular component.
Creative movement & other type classes are frequently a bit more free in terms of movement & discipline, but evaluate cautiously that you're not paying serious dance type fees for something that's too much of a free-for-all. Creative movement classes can be an absolute blast for the kids & may be a really great fit for kids who are ultra-wiggly & have a hard time settling in to much structure yet. A well done class may even squeeze in a snip or two of ballet or jazz, possibly some footwork that can lead into tap foot movements.
One thing that disturbs me about OP's description actually has nothing to do w/ dance ability. If you're going to pay someone to teach your child, in this case a very young child, they should have at least a solid basis of relating to a group of children, knowing what children of that age are generally capable of & a handy dandy bag of tricks designed to engage the children enjoyably in moving towards whatever their learning objective is -- without continuously needing to expel children from the class. Obviously that happens even w/ experienced & skilled instructors when they run across a child who either is not ready for the situation or possibly has some challenges that can't be addressed in a particular group setting.
IMO if you think it's at all likely your child may have an interest & ability for dance, look for a great ballet program. Ballet is the basis for all dance & a ballet background is necessary to have good technique in other styles. Look for a really engaging teacher who almost never needs to resort to "punishments" of any kind. Don't be surprised to find out that "structured ballet training" for little ones just may mean hopping & skipping through a chain of hula hoops, swirling & twirling on tippy toes w/ tiny scarves looped around their fingers to help them build the muscles for releve' & some idea about proper hand positions for ballet or the lights being turned off so they can see their glow wand shine as they try to make their star hang in the sky to teach the beginnings of movement for arabesque. Don't be scared off because some french words are thrown at the kids or the class is intended to teach technique. I hope I've given some good examples to show that neither one of those things has to mean rows of little dancers lined up at barre, afraid to move a millimeter the wrong way & unsure what to do because they don't understand the words.
Ballet is also fabulous for kids who really aren't going to head down a years-long dance path. It can improve posture tremendously, which is important to everyone, but it can be absolutely therapeutic to children w/ scoliosis, pigeon feet, etc.
I knew that would not be the right fit for us. 
