Map from Google - French_Guiana

In French Guiana, the climate is nearly equatorial, ie hot and humid, with a rainier season from December to mid-July, but the rains occur throughout most of the year; the only relatively dry period runs from mid-August to mid-November. The climate in the country is fairly homogeneous, but the dry season is more evident proceeding from west to east. In September and October, the least rainy months, rainfall amounts to around 40/50 millimetres (1.6/2 inches) per month in the capital Cayenne, a little more in Maripasoula, 70/80 mm (2.7/3.1 in) per month, and even more in St. Laurent du Maroni, in the far west, about 100 mm (4 in) per month, but still better than in the rest of the year. In Cayenne, more than 200 mm (8 in) per month fall from December to June, and about 200 mm (8 in) in July; the total annual rainfall is even 3,200 mm (126 in). The rains come in the form of heavy downpours, which can easily create flooding.
Here is the average precipitation in Cayenne.
Average precipitation - Cayenne
CayenneJanFebMarAprMayJunJulAugSepOctNovDecYear
CayenneJFMAMJJASONDY
Prec. (mm)38032038038051039020010040501202903160
Prec.(in)1512.6151520.115.47.93.91.624.711.4124.4
Days2117222227241910551118201

To tell the truth, there would be a second and shorter dry season, called the "short March summer", which may occur even in February, but due to its brevity (one or two weeks), it's not worth relying on.
The wettest period corresponds to the months of May and June, ie at the end of the rainy season, when more than 300 mm (12 in) per month fall in St. Laurent du Maroni, and even more than 500 mm (20 in) in a single month (May) in Cayenne and Saint-Georges-de-l'Oyapock, in the east. In this period, it rains almost every day (22/23 days per month).
The temperatures are high all year round: lows are always above 20 °C (68 °F), highs in Cayenne range from 29 °C (84 °F) in January and February to 32 °C (90 °F) in September and October, which are the hottest months because they are the driest and sunniest. But at this time the humidity is a bit less high, around 65% during the warmest hours, while in the rest of the year it exceeds 70%. In the warmer days, however, the temperature can reach 37/40 °C (99/104 °F) from May to November.
Here are the average temperatures of Cayenne.
Average temperatures - Cayenne
CayenneJanFebMarAprMayJunJulAugSepOctNovDec
CayenneJFMAMJJASOND
Min (°C)232323232322222221212222
Max (°C)292929292930303132323130
Min (°F)737373737372727270707272
Max (°F)848484848486868890908886

The sunshine amount is not very good in the wet season, from December to June, when there are about 5/6 hours of sunshine a day, while it becomes good in July, August and November, when it rises up to 7/8 hours per day, and it reaches at most 9 hours on average in September and October.
Off the coast, there are some small islands, such as the famous Devil's Island, with a climate similar to that of the coast.
French Guyana is outside of the path of hurricanes, which pass more to the north, over the Caribbean Sea.

Devil's Island

The sea is warm enough all year round for swimming, since the water temperature fluctuates around 27/28 °C (81/82 °F). The sea water is not particularly clear and has often a brown colour (except in the islets that are located offshore), because of the large quantity of water coming from rivers, although it is generally clean (except in the vicinity of the cities). It's better to swim at high tide, because during low tide the part of the beach that remains uncovered is muddy.
Sea temperature - Cayenne
CayenneJanFebMarAprMayJunJulAugSepOctNovDec
CayenneJFMAMJJASOND
Sea (°C)272727282828282828282827
Sea (°F)818181828282828282828281

When to go

The best time to visit French Guyana is from mid-August to mid-November, and in particular the months of September and October, which are the least rainy and the sunniest, especially on the eastern part of the country. As mentioned, this is also the hottest period, but it is less humid than the rest of the year, and in any case the most important thing is to avoid the heavy rains.

What to pack

Throughout the year: lightweight clothing of natural fibres, possibly with long sleeves for mosquitoes; a light sweatshirt for the evening or the sea breeze; sun hat; umbrella, or lightweight and breathable raincoat.
From December to March, a sweatshirt for the evening.