If your budget allows it, then obviously the high season dates are the best. Springtime and autumn in Paris are particularly pleasant, with many days right in the narrow range of perfect human comfort (20°C + sunshine). Summer is just as desirable because although some days will be a bit too hot for comfort, this is offset by the very low levels of rain and high chance of having glorious blue skies.
The Christmas period (starting mid-November) is an exception, with the cold weather being overcome by massive romantic and festive appeal.
The low season months include all the colder periods except Christmas week, as well as August. August is low season because many locals are away on vacation ; although some clients love this peaceful atmosphere (as I do), most seem to miss the buzzing street scene that usually characterises Paris. For some clients the August heat can sometimes be uncomfortable, at 25 to 30°C around mid-day. That said it is usually a nice dry heat (Parisians love it), all our apartments have either A/C or fans , so you should sleep well.
Bear in mind that a city like Paris remains attractive whatever the time of year, so you should quite rightly be tempted to bag a 15% saving by booking in a low season month. As a reward, you’ll feel free to indulge in that much more shopping!