In most cases when you purchase a free-standing electric range, you'll be required to purchase the appliance cord separately. The sales person should ask if you need a 3 or 4 prong cord, at the time of purchase.
NEC Article 250.140 Frames of Ranges and Clothes Dryers. requires 4 prong receptacles and appliance cords to be used in new installations, but allows 3 prong receptacles to be used if the following conditions are met.
1) The supply circuit is 120/240-volt, single-phase, 3-wire; or 208Y/120-volt derived from a 3-phase, 4-wire, wye-connected system.
This will almost always be true in a residential setting.
(2) The grounded conductor is not smaller than 10 AWG copper or 8 AWG aluminum.
It's not likely your wire will not meet this condition (unless it's really old).
(3) The grounded conductor is insulated, or the grounded conductor is uninsulated and part of a Type SE service entrance cable and the branch circuit originates at the service equipment.
Again, the supply cable will almost always meet this condition in residential.
(4) Grounding contacts of receptacles furnished as part of the equipment are bonded to the equipment.
This just means that if there are receptacles on the range (I havn't seen this in many years), they must be bonded to the chassis (which should have been done by the manufacturer).
Plugging in a new electric range will not require the circuit to be brought up to current codes, so you should have no problem using a 3 prong appliance cord (in most situations).
It's a good idea to get somebody that has some experience with electrical work to install the cord, since improper installation can lead to injury, fire, and death. The basic idea is that you don't want to restrict conductivity in any way, so you'll want to make sure the terminals are tightened to the proper torque (a conductive paste is sometimes applied to insure adequate conductivity).
While you may be tempted to save a few bucks using the old appliance cord, this is usually not the best idea. Over time the cord may become brittle or develop corrosion, which can both lead to increased resistance, which leads to excess heat buildup, which leads to failure and/or fire. It's not worth the risk, spend the ~$20.00.
Make sure you read the manual before installing the range, and follow any and all manufacture instructions.
Best Answer
Yes. First, that was a very foolish thing to do... though I'd make an exception for certain built-in ovens whose guts are mainly 240V but have a small amount of 120V conntrols.
The simple fact is: The machinery which turns electricity into heat is very simple, which means heaters are inexpensive.
And one more thing: American heaters are crippled. You may notice it is 1500 watts, not a surprise. Every US heating appliance is 1500W - toaster ovens, hair dryers, curlers, heater-fans, kettles, microwaves, plug-in wall heaters, you name it. If it has a NEMA 5-15 plug, it's 1500W because that is the practical capacity of a 15A 120V circuit.
In Europe they don't have that problem. Their sockets support up to 2x what ours do, and so their heat-based appliances are bigger when that would make a better appliance. If you really wanted to ship appliances across oceans, you'd be fitting Europlugs or BS 1363's in your US kitchen. (which is possible, by the way).
So. Simply buy a European version of what you want. Done. As for the 120V unit, stick it on Euro Craigslist. Some expat may be permanently returning to the US and be willing to throw it in their container. Given how inherently inexpensive heating appliances are, I wouldn't ship it in a box.
OK, so you Really, Really Want that 120V appliance
On UK construction sites, they use 110V for big contractor-grade power tools. They use a special transformer which gives them 110v "center grounded" so each hot is only 55 volts from earth. That makes the tools much safer than 240V tools. US heat-based appliances will cheerfully run on that, as the transformers are plenty big. So get one of those transformers and you're all set. And it has resale value.
One last thing to try
If the heater is very bespoke specialty, i.e. actually built by hand in a western country, then the manufacturer may have a phone number they answer. Ask them if they market this unit internationally. Ask them if there's a procedure to convert it from 120V to 240V. Worst thing they'll say is "no", best thing they can say is "Rearrange some jumpers".