Chad has three broad seasons, and when you should visit depends entirely on where you want to go.
The dry season from November to February is the best window for most travel. Temperatures in the Saharan north are bearable (though nights can be cold), roads in the south are passable, and wildlife in Zakouma National Park concentrates around water sources, making animal sightings much easier. This is also the only practical time to visit the Ennedi Plateau and the Ounianga Lakes. Most tour operators run their desert expeditions between November and March.
From March to May, the heat becomes extreme. Temperatures in N'Djamena and the Sahel regularly hit 45°C or more. The north is furnace-like. This is the least comfortable time to travel and most organized tours shut down.
The rainy season runs roughly from June to October in the south and is shorter and lighter further north. During this period, many roads become impassable, particularly unpaved routes in the south and east. Abeche and the eastern towns can be cut off for weeks. On the other hand, the southern landscape transforms into lush green savanna, and if you are already in-country, it is a beautiful time. Zakouma closes during the rains.
The Saharan north, including the Tibesti Mountains and the Ennedi, receives almost no rain at all. Temperatures there are most comfortable from November through January, when days are warm and nights drop to near freezing at altitude.
If you are planning a single trip and want to see both wildlife in the south and desert landscapes in the north, aim for late November through January. That is the sweet spot when both halves of the country are accessible.