Paris, Wednesday, April 5tli, 1043.The marriage of the Princess Clementine has caused, from its near approach, much activity in the Royal household. The Palais Royale is fixed upon for their town residence, and it has recently undergone some necessary alteration and cleaning to accommodate the youthful couple and their suite. St. Cloud is the delicious tejour selected by the Royal Family to pass the early summer months ; as they will remove there immediately after Easter, great preparations are now making for their reception. The arrival of Prince Augustus of Saxe Coburg, (the destined husband of our charming Princess,) with his father and brother, are hourly expected, and the marriage will be solemnized almost immediately, and I believe at Fontain-bleau; from whence they are to go to Germany, till the end of the autumn, and then return to Paris. The whole of the family (of course excepting the Prince de Joinville and Due D’Aumale, who are both actively employed in the service of their country,) including the King and Queen of the Belgians, are expected to”be present at tjiis interesting ceremony. Most sincerely do I hope that her destiny will be happier than that