For the vinaigrette: Combine the vinegar, parsley, mustard, garlic, tomatoes and some salt and pepper in a blender and blend until smooth. With the motor running, slowly add the olive oil until emulsified. Put some arugula in a bowl and lightly dress with some of the dressing.
For the fry: Heat 2 teaspoons canola oil in an 8-inch nonstick saute pan over medium heat. Add the bacon and slowly cook until the fat has rendered and the bacon is crisp. Transfer to a paper-towel-lined plate using a slotted spoon.
Add 1/4 cup canola oil to the pan that you cooked the bacon in and heat until the oil begins to shimmer. Put the flour on a plate and sprinkle with salt and pepper. Sprinkle the oysters with salt and pepper and dredge in the flour, then tap off the excess. Fry the oysters until golden brown on both sides and just cooked through. Transfer to a plate lined with paper towels. Discard the oil in the pan and wipe with a paper towel.
Return the pan over medium heat. Whisk together the creme fraiche and eggs and sprinkle with salt and pepper. Add the butter to the pan and cook until it begins to sizzle. Add the oysters and eggs and cook, stirring constantly, until soft curds form.
Divide between 2 plates and top with the dressed arugula. Drizzle with more of the vinaigrette and garnish with crisp bacon.