Preheat oven to broiler on high. Add the slices of French bread to a rimmed baking sheet and toast under the broiler (keep an eye on it!), approximately 30 seconds per side depending on the strength of your broiler.
Remove from oven and add the sliced toasted bread to a large platter. Set aside.
In a medium bowl, mash up the avocado with the back of a fork until smooth but still a little chunky. Stir in lime juice and jalapeño. Season with salt and pepper to taste.
To assemble the crostini, add approximately 1 to 2 tablespoons of the avocado mixture to a piece of toasted bread.
Top with cherry tomatoes and crumbled goat cheese.