Compensation for material damage depends on the guarantees taken out in your contract, the circumstances of the accident and your level. If you are not at fault, your insurer will pay the bill and will then return to the insurer responsible for the accident.
You can choose the garage of your choice, without being forced to choose from a list of approved garages provided by your insurance company. It is the car insurance that reimburses the garage directly (assignment of debt) The amount is calculated according to the car/motorcycle guarantees that the insured has taken out.