The simple answer is NO, you do not have to replace your furnace. If the furnace was sized and has operated properly in the past, there is no need to replace it. The upgrade in air conditioner efficiency is not dependent on your furnace, as long as the outdoor air conditioning condenser and the indoor air conditioning coil are matched for efficiency.
However, because the serviceman will already be there, and because they will have to open up your refrigerant system anyways, it may be a good time to consider replacing your furnace; especially if it is a gas burning furnace which vents out a chimney. This means the furnace is most likely below 90 percent efficient, and you could probably improve by approximately 15 percent by switching to a modern, PVC vented gas furnace.
If you have an Oil furnace, you should request the opinion of your oil or service company. Some oil furnaces have outstanding records for endurance, while others fail miserably to meet 10 year warranties. An honest serviceman knows which is which.