Hi there,
Of course there is a high level of unemployment in France, but if you are a resourceful individual, you will find a way to make your dream come true. There are many students from abroad who finish their last year of study in France, especially when they want to establish themselves in the country.
I don't know what is your area of expertise, but many young French professionals don't want to settle in small towns. As a result, many rural areas in France are in need of dentists, eye-doctors, and so on and so forth.
For instance, you can establish yourself in a small French town and spend your free-time in Paris or some other city. As you said, France is a dreamy country. The rural areas are a bit overlooked, but for specialized professionals like yourself, there is indeed a lot of work. You have many doctors from Romania from Pakistan and even from Greece who actually leave their countries and fill in the spots left empty by the French nationals, in the rural areas of France. This kind of immigration is much needed because many young French nationals don't really want to live in the rural areas.
In the meantime, practice your French as much as you can. Contrary to many EU countries, you won't find a lot of people who can speak English fluently. If you can speak French like a native, it would be much easier to settle. Some people don't have much patience when they hear a foreign accent.
If you're still unsure about what you really want to do in France, maybe you can take a year off and live here just for a year, so you will know if the French lifestyle suits you or not. If you're arty and fluent in English, maybe you can enlist to give English lessons to French kids for a year. This way, you can have your romantic experience in France. Depending on the program you'll choose, you can have a flat, you will be paid and you have chances to live in the best areas of Paris or even the French Riviera. Plus, in your free time (and you'll have plenty ) you can travel around the country or even nearby EU countries (depending on your visa, so think about that ahead). If you're still a student, you can even get some sponsorship by the French government. You can apply for instance to the Teacher Assistant Program.
If you don't want to teach for such a long period of time (seven months minimum), you can teach English in English Summer Camp In France. You can teach English even if it is not your first language.
You can even be an au pair in France. ( I won't recommend it though, depending on the family you'll get, you won't have as much free time as you want, and it can be so stressful.)
So, the possibilities are endless when you are really motivated. If going to to France is one of your dreams, don't let anyone talk you out of it. Dreams are made to be fulfilled, not forgotten.