Prince Albert does indeed speak with an American accent, as do his sisters. The explanation is quite simple; American-accented English was of course his 'mother-tongue'. I think that some of us [I include myself!] sometimes tend to forget that Prince Rainier's children were 'half American' as well as 'half -Monegasque'.
Caroline and Stephanie both attended school in England for a few years. This did nothing to diminish their American accents. I took this as a very healthy sign, because to me it indicated that Princess Grace was a very hands-on mother. Only my personal theory of course.
Princess Grace was able to speak with a perfect English accent, which of course was due to her fine training as an actress at the top-rated American Academy of Dramatic Arts. Remember how she played the English wife in 'Dial M for Murder'?
Prince Rainier, whom I first met when I was about 10, [Monaco Grand Prix, which despite its location was always regarded as a part of the 'English (!) Social Season' in years gone by,] spoke English with an accent known as 'Received Pronunciation', sometimes known as 'Queen's English' or 'BBC English'. HSH was of course educated for some time at Stowe, a top English 'Public School' [NB 'English Public Schools are actually 'private [fee-paying] schools' (!)
Prince Albert was of course educated for some time in the United States, which would have further enhanced his accent.
All three princely children also spent time during their vacations with their American Kelly relations.
Hope some of this is of interest
Alex