No, you cannot force an insurance company to fix a car if they have determined it to be a total loss. State laws and insurance company guidelines vary however if an insurance carrier has decided that it is uneconomical to repair the vehicle than it is very unlikely you can get them to change their decision.
If you want to keep your vehicle and have it repaired than you can speak to the insurance company about buying back the vehicle and paying them salvage value for it.
If you have made a claim through your own insurance provider and they have determined your vehicle is to be totaled they will settle with you usually by paying actual cash value (ACV) for the vehicle less deductible and take the car so they can sell it for salvage value.
If state laws allow than your insurance company may pay you actual cash value less deductible and less salvage value so that you keep the car. You then would be free to repair the vehicle with your payment but generally the payment would not be sufficient to cover all repairs and that is the reason the insurer totaled out the vehicle. The insurance company however would not be obligated to pay any more since they "made you whole" by paying out the value of the vehicle to you already.
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So sometimes the insurance company may want to total your car, but you would prefer to have it repaired instead. In this case if state laws and the insurer allows, you can keep your car if you are willing to subtract its salvage value from the insurance settlement.
You can contact the claims adjuster working your claim if you have questions about buying back your vehicle after it has been declared a total loss as part of the settlement process. Keep in mind though that it may be difficult to find insurance for a car with a branded (salvage or rebuilt), which your vehicle would have after being totaled out by the insurance company. So you may want to call around to make sure you can obtain car insurance for the vehicle before deciding to buy it back. | 
