This study examined how native speakers of Australian English and French, nontone languages with different lexical stress properties, perceived Mandarin tones in a sentence environment according to their native sentence intonation categories (i-Categories) in connected speech. Results showed that both English and French speakers categorized Mandarin tones primarily on the phonetic similarities of the pitch contours between the Mandarin tones and their native i-Categories. Moreover, French but not English speakers were able to detect the fine-detailed phonetic differences between Tone 3 (T3) and Tone 4 (T4; i.e., low or low-falling tone vs. high-falling tone), which suggests that the stress differences between these languages may affect nonnative tone perception: English uses lexical stress, whereas French does not. In the discrimination task, the French listeners' performance was better than that of the English listeners. For each group, discrimination of the Tone 1 (T1)-T4 and Tone 2 (T2)-T3 pairs was consistently and significantly lower than that of the other tone pairs, and the difference between T1-T4 and T2-T3 was significant. Discrimination of the Mandarin tone pairs was not fully predicted by pairwise categorizations to native i-Categories, however. Some discrimination differences were observed among tone pairs showing the same assimilation patterns. Phonetic overlaps in native i-Category choices for the Mandarin tones, strength of categorization (So, 2012), and tonal coarticulation effects (Xu, 1994, 1997) may offer possible accounts of these discrepancies between categorization and discrimination performance. These findings support the perceptual assimilation model for suprasegmentals (So & Best, 2008, 2010a, 2010b, 2011, 2013), extended to categorization of nonnative tone words within sentence contexts to native i-Categories.