French breads comes in many shape and sizes, however the most iconic and commonly known French bread is the baguette. Besides the baguette, other French breads includes the Couronne, the Flute, the Batard and the Ficelle, while sourdough bread in France is called the Pain Au Levain.
The main difference between Sourdough bread and French bread is in its ingredient. Sourdough bread is leavened using a natural pre-ferment while French breads are typically leavened using a yeasted pre-ferment.

Leavening Agent: Natural Pre-ferment vs Yeasted Pre-ferment
Both sourdough breads and French breads are made using a pre-ferment, where a small portion of the flour in the final dough has been allowed to ferment for many hours before the rest of the flour in the dough is mixed in.
Sourdough breads are leavened using a natural pre-ferment or a sourdough starter where a mixture of flour and water has been allowed to mature over time, to build a strong living culture of fermentative wild yeast and bacteria. The fermentation gasses released by these naturally present microbial organisms gets trapped in the dough and causes the dough to rise.
French breads on the other hand are leavened using yeasted pre-ferments where commercial yeast has been introduced to a mixture of natural pre-ferment. The commercial yeast will outcompete the wild yeast and bacteria in the culture to remain the dominant yeast strain in the pre-ferment. The commercial yeast will also release fermentative gases into the dough which causes the dough to rise.
Wild yeast and bacteria dominates the natural pre-ferment, while commercial yeast strains dominates the yeasted pre-ferments. The natural pre-ferment and yeasted pre-ferment behaves differently in the dough, which renders differences in the way Sourdough bread and French breads are baked, and how they taste and look.

Ingredients: Type of Flour, Sugar and Fats
Although French breads comes in many shape and sizes, the ingredients in French bread is highly regulated by French law. French breads must only contain wheat flour, water, salt and yeast, while other pastries like the croissant and brioche may contain sugar and fats like butter and oil.
Sourdough bread may contain added sugar and fats while traditional French breads do not. Sourdough bread may also be made from other types of grains such as rye and spelt while traditional French bread can only be made with wheat flour.
The water content in Sourdough bread and French bread is highly varied and can range from 60% to more than 75% of the weight of flour in the dough.
Baking Process: Fermentation time and Shaping.
Fermentation Time
Since French breads are made from yeasted pre-ferment where commercial yeast strain dominates the fermentative culture, French breads ferments faster than Sourdough breads; bulk fermentation and final proofing time for French breads is typically shorter than Sourdough breads.
Shaping
Most French breads are shaped long and thin like the baguette, the flute, and the ficelle. Sourdough bread on the other hand typically take on a fatter shape, such as the round boule and the oval batard.
Flavor and Texture: Sour vs Yeasty
Flavor
The commercial yeast used in French bread making imparts a strong yeasty taste to the bread while sourdough bread leavened with wild yeast and bacteria has a more complex sourness.
The fermentative bacteria in sourdough bread releases organic acids into the dough, which imparts a complex flavor profile and sourness to the bread. French breads on the other hand, does not have a strong population of these acid producing bacteria as the commercial yeast has out compete these bacteria for nutrients and dominates the pre-ferment culture.
Texture
Since French breads are typically shaped long and thin, they finish baking over a shorter duration of time. French breads have thin and crispy crusts due to the short baking time; French breads typically makes a continuous crackling sound after being removed from the oven as the thin crispy crust cracks slightly from the contraction of the bread during cooling.
Is there a French Sourdough bread?
French Sourdough bread is known as the Pain au Levain in France, which is usually shaped into a round boule or the oval batard.
You can surely bake a sourdough French bread like a sourdough baguette by replacing the yeasted pre-ferment with a natural pre-ferment; however this is no longer considered a traditional French bread as it will taste more sour than yeasty.