I am not sure about the meaning of this sentence.
意味ありげな笑いを浮かべた
"(He) showed a meaningful laughter" ?
Is that correct?
I am not sure about the meaning of this sentence.
意味ありげな笑いを浮かべた
"(He) showed a meaningful laughter" ?
Is that correct?
意味ありげ has the same meaning as 意味がある気配 (and may be a contraction of this phrase). It means, just like you suggest, "meaningful" or in a longer version "indicative of having meaning".
笑い is more often a smile than a laughter.
浮かべる is related to 浮かぶ "to float/to surface".
Thus the full sentence is (very much like you suggested)
意味ありげな笑いを浮かべた
He showed a meaningful smile.
or, more poetically
A meaningful smile appeared on his face.
I would say that 意味ありげ comes from 意味 "meaning" and 有{あ}り気{げ} "appearing like"/"seeming to be".
Daijirin says 意味ありげ means 何か意味がありそうな様子, or "a state of appearing to have meaning", the 〜げ presumably coming from the 〜気{げ} which means more-or-less the same as 〜そう (see also What is the usage of 〜げ and how does it differ from 〜そう or 〜っぽい?), so I think "appearing to have meaning" might be a more literal translation but that "meaningful" is probably close enough.
The 笑い here means "smile" I think.
I think the transitive verb 浮かべる here means "to express (on one's face)" (def #2 at Daijisen), coming from the core meaning of 浮かべる of "to float"/"to launch (a ship on water etc)".
So I think the translation "(He) expressed a meaningful smile on (his) face" would be close.
Cypher and userxxxx have covered the grammar but if you were struggling with "a meaningful smile" then perhaps it could be translated as:
he wore a pregnant smile on his face
or, perhaps, dependng on context:
he allowed a pregnant smile to cross his face
笑い can be smile, chuckle, snigger, giggle or smile but when I came across the following in the textbook そうまとめ文法N2:
男は 意味ありげな 笑いを 浮かべた。
I imagined a small huddle in corner, whispering, and took the line to mean:
The men let out a meaningful laugh.
(again it probably comes down to context.) The following expressions are useful to know:
自信ありげconfident laugh
自信なさげ laugh lacking in confidence
自慢げboastful